It tastes just right. We're all very neutral so I love it. I'm so excited for this trip guys because it is my first brand trip ever.  But we just arrived at LAX. We got a rental car because Ryan just wanted your rental car and I think it was probably a very smart idea so yeah it's nice to have. Very smart on your part to get a rental car. This is our reservation at Elefante. We went there like two years ago and oh my god it was so good. We dream about their whipped eggplant so we're going to go get some and then after that we're going to check into the most iconic Beverly Hills hotel. So I can't wait. I can't even believe it's happening. We were leaving our apartment this morning and I kind of started to tear up. We got one to spot so we had the most stunning view of the city. We're a traffic time so like to go eight miles to the hotel but I want to see the hotel during the day and I also have dinner at eight so I gotta get ready for that. Espresso. Yeah I was like do you have a Espresso? Like a four year Espresso martini? I just want that. Okay we're going to head back to our car.  So blue. So green. Oh yeah Ryan's color blind. Austin and everything is like gray. Oh hot. He's a hater guys. Guys we're pulling up on the playboy mansion. Dang it. You can't see anything but on the map it says it's right there. I'm getting so nervous. I have the butterflies. I don't think I can feel my feet getting numb. My whole body's numb because I'm so nervous. I have butterflies. I'm scared. We're about to turn in. It's so beautiful out here. Yeah everything's just so well cut. Well kept and beautiful. Welcome to the Beverly Hills Hotel. We are here with Amazon and I wanted to give you guys a quick little room tour. So in here is the bathroom. It's so spacious. Very classic. I think this is a TV over here but I can't figure out how to turn it on. We have a bathtub and a shower of course. I'm curious to see what products these are. You have Palmichel in there? Yeah I do have Palmichel in there. I'm not really sure the brand's here. It has their own logos on it. Oh. Very cool. Okay. So that's the bathroom. There we go. There it is. Look how big this closet is. Did you see anything? We have to put on those robes. That's gonna be so fun. Over here is the living area, the office. Ryan is definitely gonna use this desk because he saw us to work while I'm in events. Actually, the time zones are so off that I feel like you're gonna be done when I'm in the events. You're gonna be done every day almost? That's nice. We have some sweet treats. Some mini sweet treats.  Amazon decks the room out. We have some Palmichel. We have Sol de Janeiro. We have Splenda. We have Laneige. And this one. Just don't know how to pronounce those names. But over here is obviously the bed. Wait, babe, look at this. That is so cool. That is so freaking cool. Wow. Man. Iconic. You also have the garden view. Oh yeah, this is the junior suite with garden view. He said it's nice and quiet. Look at all the beautiful greenery. I always think these palm trees are like Truffula trees because they're just so long and like hairy. Yeah, from the Lorax. But it's so nice. I kind of want to explore but I want to redo my makeup, get ready and then we can explore. And then you can drop me off at dinner or something. Here's the first outfit of the brand trip. We have the stress. I'm renting it from Runth Runway. Heels are Amazon. Bag is Amazon. Earrings. I love these earrings. I just got them in from Amazon. I can't breathe. Are you nervous or what? I'm so nervous. I don't know. You want a beta blocker? I feel like I'm going to start shaking in a second. I think I just haven't really drank enough water today. Probably not smart. But I feel like after this event I'll at least know like hopefully a couple girls. So like it won't be as intimidating tomorrow. Oh my God, I just need to breathe. We are so nervous guys. Stop! Guys, I see so many cool people here. Mariana Hewitt, there's like Whitney Port. I'm literally going to ship it. Hi vlog. Can we just take a minute for the eyes? The eyes. Oh my God. It's day two. We just got some room service. And the big reveal. Eggs Benedict and Buttermilk Pancakes. It looks delicious. I feel like I'm going to a work conference in this blazer. But we're going to explore because Ryan has a little break in between his calls. And we want to like see the hotel in the daytime. So I have to vlog on my iPhone though because they are really like strict about like filming with like a big camera in this hotel which is sad. Yeah, but I feel like the iPhone will get a better angle so I'll just do the iPhone. We were going to do some exploring and maybe go to Air One, but we had room service. I'm not super hungry and maybe we could just do it tomorrow. I'm so happy the weather is getting better. Blue skies are out and I think I have like an hour until my next event or like my first panel of the day and I wanted to give you guys a little recap of yesterday because I don't think I've done that yet. You guys probably saw I was barely breathing. I was so freaking nervous, but then I went into the lobby mingled with some girls and I was totally fine after that and the venue was like so cool. It was like this long table dinner party vibes.  It was truly unreal and I met Jasmine Tukes which is like my favorite Victoria's Secret model. She is stunning and like I have so many upper makeup photos saved as inspo and her skin is just like flawless. Mariana Hewitt was there from summer Fridays. Whitney Port was there from Laguna Beach and so many, oh Alex Orle was there that octopus guy on TikTok. I don't even know his TikTok name but I've seen him pop up on my 4u page. He's currently getting really big I feel like but it was just like so crazy to be in the same room as them so I don't know. I still can't wrap my head around it. I think today we have two panels and then one event at night and I think the one at night is going to end at like 8.30 so I told Ryan we should like probably make a reservation for dinner somewhere because I think they said that they would have light bites. I'm also trying to hydrate a lot because I feel like yesterday I was getting a little bit of a headache because I was not drinking enough water.  I also lost one of my gel nails like I forgot to use primer so it just like slid off and I only realized it last night I was looking everywhere in the bathroom I couldn't find it and because I had nail glue I could just glue it back on but this morning I just found it in my purse so haha we are good to go. Oh my gosh look at the blue skies it's just so pretty also yeah it definitely looks warmer it's kind chilly but these are my favorite flowers and I I mean like there's sometimes we can see them in Austin but they're just like all over California they're just like vines across like houses with flowers and I was telling Ryan like all these houses have like really nice vegetation but Austin couldn't do that because it has like freezes randomly so it's like how freaking exciting oh I gotta bring that very broken bag we're here and I just met an Austin content creator yeah what are the chances though that's so fun. I'm from Austin yeah I was like what so we were just waiting to check in for our first event did you go to the first event last night? this is our first event and it's with is this the Alex role? no I think that's the next one okay we'll find out what this is and we will update you guys Natalie the event is outside so Cindy got her little blanket and yes box over here and I guess we need to pick some grab some sizes for you I'm a size 8 and I'm here to welcome you to our spring trend report couldn't do it without a little help from one of our absolutely favorite influencers so please welcome the one and I let's start with fashion right we are just all straight into it alright so I'm gonna be really creative and tell you guys that florals are in for spring I'm sure no one thought about that hold on the side of the street because I really want to take some pictures of these cool prom trees and he's looking on Zillow at these houses she just want to see his four beds four bedroom 6.5 million this one's 12 million here's 30 million 30 million look at the photos for the 30 million one an extra 30 here's 35 6.65 million look at his view though, downtown like hula sir what kind of hula sir we love that energy, keep it up I'm gonna go film a TikTok and take pics already looks so bougie it is time we're going to maybe I haven't tried it yet, gonna do a taste test soon and then I wanted an olipop for later, citrus so good for the best flavor then oh shoot you got it we got all messed up, but the tuna crispy rices and then the sushi sandwich, we wanted to try them both because we don't have an air wand that is a little good at all and then we also got some spring water and some wasabi most important part and also Ryan got a coffee, how's your coffee it's really good, I didn't know one this morning most friends are very good taste test time let's see oh that was good oh yeah that kind of tastes like strawberry ice cream or something rather than just a tartare I think we had tuna tartare at elefante and it was like very bland but this is like good it has like sauce, it's kind of cold but I feel like it usually doesn't really come like hot so what's our rating for this literally I was going to say 7.5 cheers I think I like this better only yeah because there's yeah there's salmon I think it's still pretty good what all I got at the first event of the day we got two pairs of Reeboks what do you think I don't have these give some somewhere though yeah I mean I have Reeboks but they're more like new balance style I feel like and then these ones colorful ones in this bag we have a whole bunch of products I have no idea how to save this brand so Sulawu Sulawasu there we go, gentle cleansing foam we have the renewing cream ooh fun new nails ooh we got Alex Earl's Amino Lean I don't wait what is this just energy I don't really do pre-workout is that pre-workout Amino acids help build your muscles and repair cool oh Lenege Water Bank Sulawasu Sulawasu Sulawasu renewing serum enice free hyaluronic acid serum I just am not going to save the brand anymore anymore activating serum this one's Dewy Glow Jelly Cream guys how am I going to oh hell yeah we got a Lenege lip sleeping mask how am I going to take this all home just blend up a cute little hat palm tree hat Splenda Monk Fruit Palm and Chilchamp and we got the Brazilian Bum Bum Sprays which one did I use in the shower I need to smell them all but whatever I used over there it smells amazing and I'm hoping one of these are the set but yeah that's it that's what was in my goodie bag and now I'm going to get dressed for a panel and then the Sunset Soiree so the panel we have Alex Earl and Girlboss Town on that and then the Sunset Soiree is hosted by Charlie D'Amelio and I just saw Helen Owyn, Alyssa Lynch and Sammy Clark Sammy Clark like does the form app like she's a fitness girl and I did form for a while so that was literally what I did is like walk past this and I was like I froze up and they're just like trying not to stare I was like oh my god that's really them so that was really cool I was so stunning to steam my outfit for tonight so let's go do that Day 2, what event is this like I don't even know we're all wearing neutrals so I love it I know we're matching each other I'm not taking it out oh energy drinks that's probably very needed I know Hello I know right yeah that's okay you all look fabulous I hope you feel as good as you look here's a mic for you hey everyone and then next up let's go ahead and welcome some ladies that you may recognize first up is Robin Del Monte of Girlboss Town thank you so much, something more than just another face with another TikTok audio so I think using my voice was super important for gaining that audience on TikTok and that's kind of how it all got started and when I say consistent by the way I don't necessarily mean just in terms of like posting cadence I mean maybe when you're posting content are you in the same bedroom with the clothes in the background right are you essentially you want your viewers to see you as their friend and so you want to do things in a very consistent way how you address your audience right is there a certain like phrase you know it comes to mind that you know off the top of my head Ronke Barnes who's a fantastic influencer she always says time to get dressed and just like by way of knowing that I am a part of her community since we're already want you to join us with so definitely grab some food, some drinks from the party because my toes were about to fall off like they were so frozen but Ryan and I are gonna go to Doe Bricks and see what it's all about how far is it about a mile and a half hopefully there's not like a long line cause I'm really hungry and I have a bit of a headache I just took some headache medicine so hopefully it won't be horrible but let's take that water I'm also feeling like I'm not drinking enough water so Air One water is coming with us I didn't realize it was carbonated when I bought it but it's okay so we're pulling up on the Oppenheim group if you guys watch Selling Sunset on Netflix I recognize the FD Jordan store I was taking a video of this with my friend that turned the camera on accident and saw Oppenheim so we had none of that too Here it is The Oppenheim group Wow Oh someone's in there Which one real estate agent This is a really cool street Sunset Boulevard Probably been here before but just don't remember We're pulling up Let's park in We're gonna manifest some parking We got this We found parking guys Don't ever doubt me Not that I was parking but you know I manifested for us Is Day 3 or 4 or I don't know It's our last day here I'm sad We're gonna go get some breakfast Ryan He was like Shutting me We're going to eat at Great White It's actually been saved on my Instagram for a while now so I'm excited to go and it looked really good So me just posted about it yesterday I think she went yesterday for breakfast so Let's go I've heard of this place called Grasseas Madre It's right there I just can't get over all these palm trees and the blue skies The air is so clean and green But it doesn't rain often This restaurant is such a vibe And I can't believe we're so alive because it's 8 8.45 but it is 10 back in Austin And I just got a matcha Ryan how's your coffee Let's get out of the honey in it I like honey in my matcha I've had a matcha in so long I feel like it makes me a little anxious sometimes so I feel like I shouldn't drink I got done with breakfast and I think we're going to drive around a bit because Ryan only has to be back in like an hour or so for a call and yeah that really helps it's just so nice like this whole area is so pretty We just packed up the whole room in 20 minutes because we were like oh my gosh we have to get out but we did get like a later check out it was at 12 so that was really nice but my event starts at 1 so I don't know what we're going to do I'm just like hanging out here in front of the car and yeah I'm really sad to leave because this hotel is like number one iconic and so homey you know like I feel like every other hotel I've just been like okay I'm ready to go home but now I'm like wait I could totally live here there's a lot of space in here but I got all my goodie bags didn't leave anything I don't know how I'm going to actually take it all back because my suitcases all feel really heavy now it's going to be a good day this is the outfit I kept my hair straight because Ryan said he liked it so I just did that and I also didn't really have time to curl my hair shoes are Steve Madden jeans are a citizen of humanity tank top it's like racer tank top it's from Mesh He and then this is from Revolve I think it's like lovers and friends just checked out of the Beverly Hills Hotel but the Amazon events are not over yet and they started actually 1.30 so we have like an hour to kill and last time I was in California the one thing I wanted was salt and straw because I've heard of this ice cream for a while and I didn't realize it was in LA and last time I didn't get the chance to come all the way out here from Irvine because like with traffic it can be like an hour and a half sometimes so we just stayed in Irvine last time but I was like ooh should we get ice cream I'm really hungry like breakfast was very filling so we are getting some salt and straw finally trying it I swear all my travel vlogs always turn into food vlogs I don't remember if I vlogged it or not because I was doing a little take talk but I got Honey Lavender and the Salt and Molten Chocolate Chip cookie dough and that one is the best and it's so freaking good like the chip it's just very well cooked you know what I mean like if you buy cookie dough ice cream at the grocery store you can have cookie dough in it but it's like really good back at the hotel and it's raining outside so I think they're moving everything indoors right in here an opportunity that you don't have in a static post to evoke certain type of emotion and obviously you can play with strategy like building anticipation the one! voice is in the back of your head it's just something that you shouldn't really pay attention to I'll just try to focus on the gun I'm gonna say that next time is it raining? no it's a spring spring sprinkle so that's a wrap on the Amazon influencer program spring favorites event it was insane I don't think I'll ever get over this weekend to be honest the last two panels I went to was with one girl that I knew from actually like to know it for years her collages are everywhere and she was so nice her name's Jen and she's so insightful like so helpful she like stayed after and just gave us so many tips and I was like wow like you are so kind like so genuine and then of course we had a Paris Hilton panel but unfortunately it got rained on like today wasn't even supposed to be the rainy day so that really sucked because I think she probably would have talked for a lot longer if it wasn't raining then we got the Paris Hilton and like a cutting board I'm like I don't know if I can even take that home but it's super cool and I don't read but I might read this because I'm like okay now I kind of want to know her secret she was saying she like spilled some tea in here and I feel like a book about Paris is not going to be like super hard to read so we'll check it out we'll see but I told Ryan I was pooped I'm so tired and it doesn't help that it's rainy even though there's like blue skies and it sucks that it rained today especially the last day but we are going to Chacha matcha even though I had a matcha already but that was like at 8am it's currently almost 5pm and I've been wanting to try the chai matcha I watched this girl on youtube her name is Jason Marie you probably know of her she's one of my favorite youtubers and she's also on tiktok but in her youtube vlogs when she comes to LA she always gets like a matcha chai so or a chai matcha or if it's like on the menu or if she just orders that like a special menu item so we'll see if it's not on the menu maybe I'll just get like a chai because I already had a matcha today but I'm excited to check this chacha matcha out I had it in New York and it was pretty good I got like the lavender one but I want to try something different today so that is what we're doing and then at 7.30pm we have a reservation for catch LA I have heard so many things about it over the past years finally going they have like sushi steak like everything so I'm excited to eat some sushi tonight I don't know if I told you guys this yet but my grandma actually lives in Irvine so I'm extending my trip I'm going to visit her and all of my other moms side of the family so that's gonna be really fun and we're actually leaving tonight right after our reservation and that's why I made our reservation kind of late so we could be traffic and just like drive there in the evening because right now we looked it up and it's gonna take 2 hours and 20 minutes if we leave right now which is insane because I don't think I think the last time we came and like took 1 hour and 15 minutes and I was like at like 8 or 9 or something so I don't really think it even takes that long but hopefully we will not hit traffic on the way there but if we do I guess that's just a lie am I surfing in the south? the skies are so blue right now it's so sad that it happened during that last panel but... you want to tear something? not on the icon it's getting rained on we're off to our final destination for our food tour of LA what has turned into a food tour and I think I said this before but we're going to catch we're calling her amma and I know that's like actually language but for some reason we all call my grandma amma so I don't even know what rating do we give cat? it was pretty good guys it wasn't over hyped and I was really really worried about that because when you go to restaurants I mean I guess this whole trip I've been going to restaurants that I've heard about on tiktok and stuff but it was definitely pricey definitely the most expensive right? oh here? yeah here but it was a good one, went out the bang in LA and now we're in Irvine for the weekend until Sunday and we're just going to have like a wholesome weekend I don't really know what we're going to do but all I know is that I want to go to Laguna beach one day because we went there the last time he was here and we loved it we just like loved those little beachy areas I mean they're all so different Santa Monica, Venice beach Huntington beach Newport, Laguna did we see all those beaches this time? you were here? oh my god I don't think we went to Huntington when you were here last time we went to Venice I'm going to end this vlog here and start a new one but I just wanted to say a big thank you to you guys and just anyone who supports me because it really really truly means so much to me and if you guys don't already follow me on tiktok and Instagram and all the things and my Amazon storefront I will have it linked down below you can actually follow me on Amazon so you can be like what I did of what I add to my storefront and all the things so I'll see you guys on those platforms and in my next vlog, bye


Hi, I'm Zor. Welcome to Unizor Education. I would like to continue solving problems related to logarithms and exponential functions. Maybe these problems just may be a bit more difficult than the previous lecture. Well, in any case, I think it's very important to basically be prepared for any kind of ingenuity the problem creators came up with. So let's not be afraid of this. It looks a little scary maybe in the beginning, but believe me, it's not really very difficult at all. All right, so I'm sure you have spent some time looking at these problems before listening to the lecture. If you didn't, just pause this video and I strongly recommend you to try to solve these problems yourself. They are all in the notes for this lecture on Unizor.com, so go ahead and try to do it yourself first. Then listen to this. All right, so problem number one, 0.5, 5 over 3 minus x times square root of 2 minus 0.25 to the power of 2 minus x equals to 0. Well, what you really have to notice here, this is one-half, well, somehow related to number two, right? This is square root of 2, also related. This is one-quarter, also related to number two. So let's bring everything to the powers of 2. I mean, that's exactly what kind of unifies the whole equation and will make it much better. So what is 0.5? It's 2 to the power of minus 1, right? That's one-half. And then I multiply it, I mean, I raise it to the power of 3 minus x, okay? Square root of 2 is 2 to the power of one-half, minus. One-quarter is 2 to the power of minus 2. Minus will inverse it to one-half and 2 will square it, it will be one-quarter. And this is to the power of 2 minus x equals to 0. Now, when you raise to the power and then raise to another power, you multiply the powers. Remember this, right? So it's basically 2 to the power 5 over x minus 3. I reverse the sign here. Minus 1 times 5 over 3 minus x is 5 over x minus 3 times 2 to the power of one-half. Now, instead of having minus and then equals to 0, I will add this thing to both sides. So I will have nothing here and it will be on that side of the equation 2 times 2 minus x. Now, if you multiply two exponential expressions with the same base, you know you have to add the exponential part. So it's 2 to the power 5 over x minus 3 plus one-half equals 2 to the power minus 2 times this. It's 2x minus 4. And now, we basically go to a very easy thing. Since these two exponential expressions with the same base are equal to each other, it means their powers, exponential parts, should be equal to each other, which means we can go to this particular equation. Obviously, you can multiply both parts by x minus 3 and you will get a quadratic equation. Now, what's wrong with this solution? Well, let's finish it up, actually. So it will be 5 equals 2xx minus 3 minus, one-half would be here, so it's 9 seconds times x minus 3, right? Well, you probably should multiply by 2. So it will be 10 equals 2x square minus 6x. Well, we have to multiply by 2, so it's 4 minus 12x minus 9x plus 27. 9x 27 to multiply here 4 seems to go like the right equation. Alright, so simplifying it further, we will see that this is 4x square minus 21x plus 17 equals 0 and solutions are 21 square is 400, 441 I guess, 441 minus, 4 times 17 times 4 is 40, 28, 68 times 4, 70 times 4 is 80 minus 8 is 72, something like this, if I'm not mistaken. And 441 minus 272, 441, 272, it's 9, 3, 6, 1, 169. 169 is 13 square, which is very convenient, so we can actually have plus minus 13. So what are our solutions and what's wrong with them? One solution is 34, 8, or 17 fourths, okay, 17 fourths, and another solution is, that's 8, so it's 1. So we have two solutions, okay. I'm not saying something wrong with them, but what's important is to analyze these solutions against the domain of the original equation. So let's go back to original equation, which is this one, and think about if there are any restrictions on these things. Well, the exponential function can have any argument. So the question is, what's the values of arguments? So x not equal to 3, that's the condition here. Now here, we don't have any restrictions. So basically both are fine, and both are satisfied this particular condition, which means that's the right solutions for this particular equation. That's it. It's very important to check your solutions against the domain of all the functions participating in the equation. 4 to the power of 3x equals 3 to the power x square times 2 to the power 3 minus x. Well, incidentally, we don't have any restrictions on the value of argument x here, because these are all exponential functions, so everything is cool. Right, okay, what should we do about this? Well, the best thing is to apply logarithm to both sides, left and right. But before doing this, I would probably convert 4 into 2 to the power of 2 to the power of 3x, which is I have to multiply the exponential part. So it's 2 to the power of 6x equals 3x square times 2 to the power of 3 minus x. Now I will apply logarithms, base 2 probably would be the most convenient thing. So if I apply logarithm to both sides, left and right, I will have legitimate equation with logarithms. Now log 2 of 6x, sorry, 2 to the power of 6x equals log of 3 to the power x square, now this is base 2, times 2 to the power of 3 minus x. Now, what this is? Which power should I use to raise 2 to get to the 6x, obviously 6x. Now here, first what I should do is obviously represent logarithm of the product as a sum of 2 logarithms. So it will be logarithm 2, 3 to the x square plus log base 2 of 2 to the power of 3 minus x. Alright, so that's obvious. Now, this is also easy. This is 3 minus x. Now, how about this? Well, this is not actually the easiest thing to do. We would rather prefer to have logarithm base 3, not base 2. But we can very easily convert it, one into another. You remember that log A B times log B C equals to log C base 8, right? So in this particular case, I would like to convert log base 2 into log base 3. So I have to basically divide these two things by log A B, log A B. Now A is our 2, B is the 3, and C is this thing. So it will be 6x is equal to, so instead of log 2, I will use log 3 of 3 to the x square. Which is this one. But then I have to divide it by log base 3 to the plus, as I was saying, this is 3 minus x. Now, what should I do with this? Well, obviously if this is, the power can always be taken out from the logarithm as a multiplier. So my new equation would be 6x equals log 2 base 3 x square log 3 base 3, which is 1, right? So I leave it as is. Now what is this? Well, this is a quadratic equation, which we can always solve. This is just a constant, not a big deal. So I'm not going to do it. Obviously it doesn't have integer solutions or anything like that. But whatever it is, it is. Now, since original equation does not present any restrictions on the argument, both solutions to this quadratic equation actually are good. If there are any solutions in this particular case. Whatever this quadratic equation presents us as solutions, are solutions to original equation. I'm not going to go through this quadratic equation for obvious reasons, but you should do it. Let me just say that whatever I'm doing here is just a help. You really have to drive the whole thing to the conclusion and get the number, and it would be great if you can even check the results. Next. Okay. Absolute value of x plus 3 to the power of x. And then the whole thing to the power of x plus 2 minus absolute value of x plus 3. The same thing, which is important to the power of x plus 4 equals to 0. Well, again, you are raising to the power and then to another power, which means you multiply the powers. So it would be x times x plus 2. Now, this thing can be moved to the right, so it's equal. This is minus, so it will be plus on this side. x plus 3 to the power of 3 times x plus 4. And obviously, since you have the same expressions for exponential functions, the bases are the same. It means that your exponents must be the same. So x times x plus 2 equals 3 times x plus 4 quadratic equation. And now, back to the original. Are there any restrictions on the argument x? Well, no. Because this is absolute value, as you see. Which means x can be anything because this thing will always be positive. So we can always raise any number to the positive. Well, there is one restriction there. The exponential function usually is considered not only for positive base, but also the base not equal to 1, because then it makes it trivial. I'm not sure if minus 2, that what makes the base equal to 1, if minus 2 is the solution. Well, actually not, because minus 2 will nullify this x plus 2 and will not nullify this. So minus 2 is not a solution. So even if you want to restrict our solutions to non-trivial cases, we still have this quadratic equation as the good one to represent solutions to original. But you see, all these problems, they really look a little scary from the beginning. But when you think about them and you find that there are certain ways to approach them, it doesn't look as scary at all. Next, log x. Now, this is a common or decimal logarithm, since I don't use the base. Minus 2 log 4 third equals 2 log square root of x minus 1. Well, here we will have to do the reverse instead of using the log to convert exponential to the plane one. We will use exponential to convert log into a plane equation. Now, here is how to do it. The difference between two logs is a logarithm of their result of their division. So this is log of x divided by, here I will immediately insert that to inside, so it will be log of 4 third square, right? And which is 16-19ths, so it will be 16-9ths, I mean, 16-9ths. That's how it will be, right? Because 2 log 4 third is equal to log 4 third square, which is log of 16-19.  That's simple, so that's on the left. What do we have on the right? Well, similarly, we will put these two inside the log, so it will be log square root of x minus 1 square. Now, two logs are equal, which means the arguments are equal. 9x over 16 is equal to, and this I can always represent as x minus 2 square root of x plus 1. How to solve this equation? Well, you assign this, and what you will have? You will have 9y square 16s equals y square minus 2y plus 1. Now, this is a quadratic equation. Now, what's wrong with this picture? Well, in this case, we are actually restricted by the original equation. What's the restrictions on? Forget about this quadratic equation. We're not going to solve it. You do it yourself, but whatever the roots of this equation are, you really have to look back at the original equation. First, log exists only for positive arguments. So that's what this gives us. Here, not only x should be positive, so square root of x actually exists. Also, square root of x minus 1 should be positive for log to exist, which means square root of x should be greater than 1, and considering x is a positive thing, so it's x greater than 1. This is the final restriction on the argument. Whatever roots that particular quadratic equation produces, whatever solutions you can find, they always should be checked against this. And only the solutions which satisfy this inequality are real solutions to this equation. So you should never forget that certain equations actually restrict your solutions. And that's why you have to do the checking and the verification of the domain, etc. x to the power a log x plus b, now it's also a decimal or common logarithm, equals to cx. Well, so far as you see, the only restriction is for this log, x should be greater than 0. And no other restriction succeeds because you can... Well, I'm sorry, there's another restriction. This is the exponential function, but it actually gives exactly the same thing, x is greater than 0. So this is the only restriction. Now, how can we solve this equation? Well, let's just logarithm both sides. Can we do it? Well, a little nuance, c must be... It's just a constant, right? c is a constant, but the whole solution exists only in case c is greater than 0, obviously, right? Because otherwise, the left part is always positive and the right part should be positive as well, therefore. So whatever constants are provided in the beginning as conditions for this particular equation, this is one of the conditions. We don't have to check our solutions against this because this is a constant and supposed to be given, but it's supposed to be given even in this particular range of ways. Now, we can apply the logarithmic function to both sides, left and right. If arguments are equal, logarithms are equal. So what's the logarithm of this thing? Well, this is something to the power of something. The power goes outside of the logarithm, so we will have a log x plus b and then log x of this one, right? So that's on the left. On the right, we have log c plus log x because logarithm of product is sum of the logarithms. Now, what do we have now? Obviously, a quadratic equation. If you will assign the value of y to log x, you will basically have a y square plus b y equals log c plus y. So this is a quadratic equation, so you can find the values of y. Now, obviously, values of y must be converted into values of x. x obviously is equal to 10 to the power of y, right? From here, this is the base 10. So 10 to the power of y is x. So once you find y in this particular equation, this is the solution. And again, you really have to worry about c being greater than 0, and that's supposed to be given. And as a result, by the way, as a result, since x would be 10 to the power of y and y is whatever it is, this is always positive. So the condition x greater than 0 will always be satisfied because of this. Alright, move further. We have one more problem for this lecture. Log base 2 of x plus 12 times log x of 2. What's obvious here is this thing, as I'm sure you understand, can be converted into y. Well, obviously, log 2x times log x. 2 is equal to log 2, 2, which is 1. This standard conversion, which I have used many times and proved that particular conversion in one of the lectures, right? In this case, a is 2, b is x, and c is 2 as well. Now, using this, we can rewrite this as or multiplying by log x. You have log 2x plus 12 equals log 2x times 2. Now, what is 2 times log x? If you want to put this to under the logarithms, it's x squared because the power is factored out in this particular case. And since logarithms are equal to the same base, then you have an equation x plus 12 equals x squared, which is a quadratic equation, and you can always find it. Now, again, what kind of restrictions we have? Well, obviously, this one, x should be greater than 0 and x should not be equal to 1 because only these bases are allowed for logarithms. Now, this x plus 12 should be greater than 0, but this actually is enough to satisfy this equation so there are no other restrictions. Now, here, you have to find out if these two are satisfied. Now, what's the solution? x squared minus x minus 12 equals to 0. So, that's what? 4 and minus 3, right? So, x equals 4 and x2 is equal to minus 3. Am I right? 4 is 16 and 9 plus 3. So, this one is not good because of this condition. Well, that was the last problem I wanted to present today. I do suggest you to go again through these problems. Solve them yourself completely from the beginning to the very end. Make sure you check against the domain of the original equation. Check the results of your calculations, whatever the solutions you have. Put it into the original equation and see if it really satisfies because you see we are doing certain transformations of these equations which are not always invariant. So, there is an interesting lecture about invariant transformations which I put into the equations category. If transformations are invariant, they do not change the solutions. But if transformations are not invariant, that might actually present extra solutions. Just as an example, let me deviate slightly. If you have an equation x minus 1 is equal to 0, the only solution is x equals to 1, correct? Now, what if you will do it differently? What if you transfer into this and then squared? And you will get this equation. Now, raising to the power of 2 is not invariant transformation. And this equation already has two solutions. And this one is not yours. If you will put it here, you will see that this is not really checked. So, non-invariant transformations might actually add you extra solutions. And in some cases, you might even lose certain solutions if you are performing an invariant transformation. So, you have to be very, very careful about this. I might actually spend a lecture about non-invariant transformations, about how they add or remove certain solutions if you are making non-invariant transformations. But this is not about this particular lecture. That's for the future. Thank you very much. Using this website unizord.com, I do suggest you to register and take exams. Then you will need a supervisor or a parent who will enroll you in the course where you will take exam. So, that would allow you to much better control the educational process. Thank you very much. That's it for today.


ESP – English for specific purposes This term is used to define a section of the English language industry that includes courses or curriculums that are designed especially to be used by distinct groups or professions. Common examples of general ESP courses could include scientific English, technical English, and business English. As the use of the English language continues to grow around the world, many areas of employment are becoming increasingly reliant on its usage. To meet this need, there are numerous courses available that are aimed at specific professions, such as medical practitioners, air traffic controllers, and various branches of the hospitality industry.


That's right. Played in the league 17 years. He's a champ. He's a defensive player of the year. He's meta world peace and meta. I got to tell you, I love when we have guys on that spend a little time with Louisville because he's a very secretive man. He doesn't like to share too much. So if you could just give us a little bit about Lou. What was it like spending time playing with him? Man, shout out. Good morning, everybody. Playing with Lou, man. It's been great because I was at the end of my career. I was kind of going through an identity crisis because I wanted to still play, honestly. I'm so competitive, but Lou always kept things in perspective and he was a leader to the young guys. Lou was like a leader to the older guys and a leader to the young guys. I mean, it was a joy. It was like, you know, kind of built a great relationship, you know, even though we didn't see each other much after. I went back to school, did a bunch of other things, but, you know, Lou definitely stands out for sure. Hopefully that wasn't too sentimental, Lou. Yeah, Louisville, all right. No, that was, that was perfect, man. Our times playing together was an experience, man, between us trying to bring the young guys along, farewell tour and trying to stay competitive at the same time. It was definitely, it was definitely an eye-opening experience and we built great relationships out of that.  He spends a lot of time around you and your family. Yeah. So, you know, we developed, we developed great relationships out of that experience. For sure, man. I love to take care of them. Yes, that's my little dude, man. Every time he come over, he, a lot of energy. He might be a six man like you, man. He might be a six man. Yeah. Yeah. He hasn't picked, he hasn't picked that ball up yet, but, but I'm giving him some time. So, yeah. That's, I like that. No pressure. All right. Your first stint with the Lakers was with Kobe. You guys won the championship. Can never get enough Kobe stories. What was it like to play with him? Did he make you better? What, what are your biggest memories? Well, I love Kobe, RIP Kobe. He was, Kobe is so competitive, honestly. First time I got there, you know, we didn't have much to say. I think he wanted to see, he just told me, don't mess it up. He didn't tell me that, but I've never heard much from Kobe. I mean, I knew the Triumph. I learned, I kind of, I was a math major too, so the concepts made sense. So I caught on to the triangle like right away. And then other than that, my work ethic was probably second to none. I made Kobe just probably up there. So other than that, we just talked about the game. We never really went out, never had lunch, none of that stuff, no dinner, but on that court, we was, we were synced. The second year after that was kind of tough, but Kobe overall, you know, seeing them in the gym at 5.30, we heard these stories, 5.30 AM, working on that Japs step, working on that pivot, you know, all that type of stuff. That's Kobe.  And then you come back to Lakers for a couple of seasons. What was different when you, when you saw Kobe, the second go around, what was different with him those two years than compared to the first four? He was way more fun. You know, like I was talking to him to my career. I was in, I had a little knee injury at the end and then Kobe was just trying to finish out his career. But he was way more fun. The second time he was talking to rookies, laughing a little bit. And you know, my first thing with the Lakers, that wasn't so, you know, he was just really, really serious all the time. But it was good to see, it was good to see him just kind of let his guard down a little bit, even though he's still a compete when he was in the games, as we saw. But I was happy to see that he let his guard down. Matty, in 2010, you won that championship with the Lakers and hit that huge game seven three ball assisted by Kobe, actually. What do you remember the most about that shot? How special was that shot? It was crazy. It just summed up my career. I mean, I got a big ego when it comes to basketball. I think I'm better than what I am, but I needed that bad. Like I needed that championship to fill my ego. Because I don't know, honestly, I don't know if I would have been able to live with myself without a championship. I got one is not enough. And he's like, you know, it was kind of surreal that he passed the ball to the right.  I remember that playoffs. I was actually with my therapist. She from Houston. So I flew her in because you just kind of be ready. Some games you taking four shots, some games you taking two shots in the playoffs.  So you just got to play in a rhythm and playing in a rhythm is going to look bad with a stat sheet because you playing in a team rhythm, but your shots is not following. You just got to try everything, deny, box out, correct passes, sprint back. You got to try to do all these things that don't show up in the stat sheet that you get no credit for. And then on top of that, squaring up, right? Squaring up when the ball comes, let it go. Some days you gonna look bad. Some days you gonna look good. And that was just like, probably, you know, just summarize my career, getting defensive player early, you know, being an all NBA team, all start early and then going through the broad and kind of awards going away, all the stuff, all the recognition going away. Even though I was still getting awards at that time, that championship just like, I just couldn't think. I didn't think the basketball gods would ever give me a championship. You know, we've talked about you playing with Kobe and winning the championship, but throughout the course of your career, you've played against them almost 30 times. What do you, what do you remember about those, those battles? I remember about him winning 70% of those battles. I got him calculated in my head. I got the first battle in Chicago. I blocked his shot to go in the overtime. It was a great block. It was crazy block. But other than that, he won the rest of the battle. So it was playing against Kobe was crazy because he wasn't lightning quick, but he was just so mentally tough. So he, he will wear on you mentally. So those games, you know, I think maybe once or twice, I went out the night before, but for the most part, I was never going out the night before playing this. I was sleeping and getting my rest because you're talking about a 50 piece. Hey, you don't want to be on the other side. That was your matchup. Yeah, that was my matchup all night. I love that it circled like, don't go out the night before that. Okay. You know what lists do to sports fans and all of us who do this for a living. We love lists. We also love to see who's left off of lists. So you did your top 10, not that long ago, but in the top five, neither Kobe nor LeBron was on the top five. Did you get heat for that? And talk to me about who, who is your top five?  That's changed a lot, but shout out to LeBron. I love LeBron, you know, and Kobe. Obviously, I played with Kobe and I live in Los Angeles. But I think you got a guy like Will. I'm changing. He's number one. This is God. Yeah. But when you got a guy like Will, Will only averaged 13 points this first season. So everybody's saying he played against firemen. Well, those firemen kept him to 13 points and then 20 the next season. Will put in so much work where eight season later, later he averaged 50 and will also play it against Karim Al-Dujabal and Karim played it. You see, I'm saying so from that perspective, Will blocked a lot of Karim shots and we put Karim as number one sometimes. So you can't forget about the dead. You know, Will was a dominant force. And then Bill Russell with those 11 championships, even though he wasn't a scoring, he wasn't scoring a lot, but he also averaged 22 rebounds along with Will. I think that's number one. You know what I'm saying?  Magic. Yeah. People sleep on magic and magic is he's older. He's a politician. He's gonna, he don't give himself a lot of credit, you know, but magic is asleep with magic. You look at magic stat line, you know, his awards, he was a, he was the man on that team. You know, magic, they don't get over the hump and those five rings with the Lakers. So you got to give him some credit. And then I don't think people get shacked enough credit. I got shacked at 10 somewhere over there. You know, Shaq has already been in top five, but I think Shaq got bored with the game. Shaq stopped working hard. And that's why people passed him.  It was too easy. The same thing with Michael Jordan. Will Chamberlain, you gotta think about what he did. He said, I'm a set records so nobody could ever pass. That was the league first start. So he was already seeing the future. And I think Michael Jordan just got bored. But LeBron is doing what we'll do. So LeBron is when he retires and is all said and done. We got to give him that his flowers. There's no way he's not number one. He put in the work.  I'm not saying others are not, but I'm saying to, you know, to be with the same family that is really difficult, along with being one of the greatest players that. So I think when LeBron retires, I'm gonna give him the nod. Mehta, is it true that you crack two of MJ's ribs in a game of one on one? How did that happen? What happened? Take us through it. And I, you know, actually, I didn't release that story. That story was released by my good friend Sam Smith from the Chicago Tribute.  And we was, you know, I was super competitive. People didn't really know how what I was bringing when I was 19.  I didn't really get tired and I was super strong coming in. So Michael was just posting me up and he had referees and everything. So he's posting me up on the left block.  When Michael holds you, you can't get around. And one of the issues with Mike is if you let him touch the ball, he gonna score. So in those games, those games were super competitive. So as I was denying, I moved his arm out the way. And then the ref called the offensive foul. And so he actually got called for offensive foul. But then I hit him by mistake with my right elbow went into his ribs. And, you know, and then when I found out I broke his ribs, I was in the bed for like two days. I didn't go to practice until I summer practice. I was sick. I couldn't even get out the bed. My agent called me said, maybe you got to go to practice. I said, I broke Michael Jordan ribs. I think I can't even function right now. And then Mike called me and then Mike called me. Mike was like, Hey, man. So I, you know, that happens. I want you to keep coming back to the gym. I was like, sorry, Mike, that's crazy. Mike, Mike hit me up. Then I went back to practice. Summer practice. Would you say, would you say, would you say MJ is probably one of the toughest players for you to guard? Yeah. Mike is definitely the toughest. He's not as fast as LeBron. Don't jump as high. Not as strong. LeBron for some different. And Kobe also brings something different, very similar to Mike. But Mike is strong, efficient. It ain't like you're going to contest his shot. And he, you know, he's going to be on balance, good space. Definitely the toughest dude I've played against for sure. Who would you think? Who would you think to be a toughest guard for you right now in today's game? I look at it a lot. Man, I just stopped being competitive maybe two years ago. Man, I couldn't sleep with myself now. So man, I just stopped thinking about the game like that. But I looked at some guys career as it went on and on. Cause you can't tell the first day you see a guy the first year or even at first like entrance into being a star. So you got to give it a yes to see like, wow, you know, I think I'm not going to put no names on it. Honestly, I'm not going to put no names on it. But there's definitely a few guys I feel like I would have for sure shut down. And then there's definitely a few guys I'm like, ooh, you know, uh, maybe I don't have a chance. You know, like Kobe, you know, don't really have LeBron, you know, you don't really have a shot. You also play with one of my favorite players, Tracy McGrady. And he was so cold. And I feel like people don't talk about him enough as a one-on-one scorer, just a scorer in general. What was it like playing with him? Was he one of the hardest matchups in practice or guarding him? Cause, oh man, that's what T-Mac growing up. You know, T-Mac, T-Mac was a, he was hurt when I got to Houston. But that first training camp, that training camp was incredible because, um, the thing, the pieces we had was incredible. People forget about the Ken Bay, but the Ken Bay were average 10 and 10 when he got into the game. The Ken Bay was playing incredible before he broke his knee in the playoffs. Um, I was playing only eight minutes a game before T-Mac got hurt. Then I started playing and kind of show what I could do. But that team was stacked. Um, T-Mac got hurt, I think 25 games in. So then, but, you know, when I was playing with him, you know, to watch him play and it was pretty impressive. He could pass the ball. He could score the ball.  He's just so gifted offensively. Um, but definitely one of my favorite players. Definitely. All right, Metta, we got to talk Draymond Green for a second. Obviously, suspended indefinitely. The Nurkitsch hit was the, was the final straw seemingly there. And part of his suspension is he's got to go through some counseling. Um, you know, we all know your past.  Like, do you, do you reach out to a guy like Draymond? Would you give him advice? Are you comfortable doing that? I mean, um, definitely, I think Draymond's an elite winner. And I think that just, I want that to be highlighted.  I definitely always reach out. Anytime I see a guy getting into trouble, I don't always get a response. I used to, but, um, you know, I'm always there for any player going through anything. That's for the open line for any player. Even though I, transparently, I do have my own agencies, but I'm not trying to steal any players, but I just want to see players do well. You know, I want to see players do well. Um, I think Draymond's going through a little bit, right? Cause you're not as good as you used to be. You're not young, you're not as young as you used to be.  So I think he needs to take off the competitiveness a little bit and just have this fun, have some fun, ride it out. I was super competitive of my last year, but actually my last, it's the season before my last year, but then I started to talk more to rookies, you know, growing up in the nineties and stuff like that. You just don't have friends. You don't have friends on the court. And, and I think like if, if Draymond doesn't take his foot off the gas a little bit, I think, you know, those friendships he could, he could make and those people, he could help. There's young players out there right now that's probably like another young Draymond, right? But Draymond is so competitive, he don't see it like that. He just see food, you know? So from that perspective, I just hope he takes, takes his foot off the gas a little bit. His legacy cemented already. It's nothing else for him to prove. He's a winner. He going to be in all of it, right?  And hopefully, you know, he can take that into consideration. Matt, as one of the best perimeter defenders ever, who do you think is the best defender in the game today? Right now, you know, I like that kid Max from Philly because he's doing it on both ends. You know, he's, he's, he's super unique. Obviously, before Kawhi's injury, I like Kawhi.  I got a little salutation on my mouth when I see so many people walk away with multiple because I shot myself in the foot. I should have had two or three of them, but I'm just getting suspended all those other nonsense. But Rudy's like walking away with it. But in terms of just like, you know, on the ball, garden, I got to go with that kid Max because he's doing it on both ends. That's pretty hard. Are you talking about, are we talking about Maxie? Yeah, he's Maxie. All right, all right. I like that. Yeah, he's pretty, he's pretty. Yeah, he can score and can lock up. That's pretty high praise. All right, that's very high praise.  Obviously, I'm a huge Spurs fan, and that was a big moment for all of us. And you said he could average 40 at some point. You still seeing that? Or what, what is it that you see in him? I mean, just take away the size. That's, we all see that. But what? He's the closest to Will that we'll have that we'll ever see. You gotta remember, Will averaged 13 points this first year and 20 plus rebounds. But, but I think this kid gonna beef up. He gonna get better.  He gonna go get 101 at some point in time in the next seven years.  Yeah, he's gonna, he's gonna for sure catch a rhythm where some rookie that can't guard, don't know how to deny, can't backdoor, making a ton of mistakes. And boom, 101 piece, averaging 40. I think you don't see it from here. Okay, there's a banner race for that. I don't want to hear any argument. If you get 101, you get a banner. Absolutely. Absolutely. I think he, I think he gonna be, even though Chet having a better year, but he's on the way by the team. Yeah. So I think it's gonna be special, especially when he beefed up. Remember Giannis, I didn't know Giannis wasn't here. I didn't know this kid was, he's just some string being running out there. Now he's like a force. I think this is this year. I think women, Giannis gonna be like that. Metta, you also gave really high praise to Jalen Brunson, saying he could be a top seven, I think Nick player of all time. What have you seen from him just to kind of, to justify that and to see so much of him? Well, he's young. He's putting up numbers at a fast pace. And then also, you know, I think in a garden, it's hard to play in a garden, as we know, the rim strengths in the garden. For him, it seems like it's wide open. Like he's super confident, not worried about the fans, not worried about the fair weather, Nick fans, you know, we are all bad bandwagon fans in New York, all of us. This kid seems very comfortable in the lines there. So you got to imagine he's gonna do this for a couple more years. And I got to imagine that other free agents see this and they're like, okay, I want to compare him because he, the leader looks very comfortable. Obviously, Julius Randall's really playing well in the garden also. Now, it's not easy to play well in the garden.  You know, how many point guards? Not many, maybe Mark at some point in time. You know, so I think this kid is gonna, for sure, be in the playoffs championship, you know, we'll see. But they're for sure being the players that get past the first round at some point, they might make the Western Conference finals. And at that point, it's all about, you know, the players you have on the team, the coaching is pretty solid. You know, so I think he's gonna walk away with at the end of his career.  You can see him being a top knit all the time. Nick's fans everywhere are very happy. Madda, before we let you go, you were on The Masked Singer, a show that just perplexes me, honestly. You were the cuddle monster. How does that come about? I didn't know, you could sing? How's that happen? Yeah, Lou told me how to sing. You know, Lou got bars. It was fun. I try to stay off TV, honestly. But, you know, I'm always getting called to do TV. And then I told my wife, I don't feel like doing this one. And then my friend said, dude, it's gonna be fun. Then my daughter was like, you got to do it.  I said, cool. Yeah, I'll do it. And then when I got there, I had way more fun.  I do like to entertain. But now they I'm just not interested in anything television. But um, but that show is that show is fun.  Yeah, we all sound good. Everybody's out here in the shower. They put a little auto tour to my voice. I was like, all right, we good. God, that's awesome. Yeah, that would be a fun one. I'd like to see everyone do. Madda, I know, I know you just said you don't want to do TV, but we appreciate you doing it this morning. Hopefully you'll come on again. It's been a pleasure. Absolutely. Thanks for having me, Lou. My dude. My brother. Good to see you. Good to see you. Yeah, you have a great season. All right. Thank you, sir. We'll be back with that man. How's the family after this?


The reason I volunteer for veterans is my grandpa. I'm very proud of him and everything that he has done. He's a model citizen, a model veteran, and I just want to be able to help more people like him. He started talking to his grandfather about Vietnam and he felt that veterans just weren't getting enough. He already had it in him just to be a very kind and amazing human and soul. But his grandfather is a veteran. I'm a veteran as well. And he knows what we've gone through. He gets it. And a lot of people can get it, but they might not expand on it. And he really has. Jacob is an outstanding young man. I mean, he started to volunteer during COVID when people were staying home. He was coming in to drop off comfort items for our veterans. He's come in with Christmas cards, Valentine cards, cookies, letters. He's written personal letters to all of our veterans. He cares that much. It means a lot to us. Working with veterans has taught me to grow as a person and be able to help people as often as possible with whatever you can.  I like hearing their stories and I love how it feels when I'm able to help someone. He's using his passions through volunteering to help drive where he wants his education to go. I plan to study supply chain management at Michigan State University and I truly hope to one day be able to carry over the skills I acquired there to the VA. I really would like to just work with veterans throughout my whole life and keep building with them and just improving their conditions going forward.


Hi, everybody. Joe for Jasper's Case Breaks dot com. We did it. We knocked out a case, a half case, actually, of 2021 Panini Prism Football, six box half case picker team number seven, which is from a fresh case. Remember, in the picker teams, all card ship. And I think picker team eight is already down to single digits. We may be able to run that back straight up. No filler. Big thanks to this group here for making it happen. So if you have a rooftop next to your name, that means you won that spot in the filler, the team random. So thanks everybody for getting in. Now let's grab this bulky case here. It's not super heavy, but it's a little bit of an awkward size. So let's pop this open and let's see which six boxes we're gonna do. All right, so there's six boxes on the left side, six boxes on the right side. We're gonna select a die, I like that one over there. We'll select this die, one, two, three for the left side, four, five, six for the right side. Five, one, two, three, four, five, six. So this we will reserve for picker team eight. We'll mark all these PYT so we can differentiate them from the random team boxes I have back here. In fact, I'm just gonna leave this off to the side right here. We've got a good chance at running that back shortly. Four around here. All right, picker team seven, good luck everybody. Two autographs per box on average and picker teams all card shipped. So settle in, let's go. We got a little baseball on the background. Brian, can I post teams? What do you mean? Oh, here's a list once more. Picker team seven, there you go. There's also a DVR function, Brian. And you can rewind on the stream to see the team list. And then, but just make sure you're back live. Logan, what's up? Logan's asking, who'd be the best second QB in 2022? Zach Wilson, who are you assuming is the first best QB? Gilo, what's going on? How are you? Color blast would be nice. There's Devonte Adams to 75. Oh, second year QB. 73 out of 75, Green Bay, Sean Matic. Tony Romo, and we got Rondale Moore. Cardinals. It's Ryan with the Cardinals, won that spot. I wonder if he gets more looks. No Deandre Hopkins for a good chunk of the season. Christian Kirk, I think signed elsewhere. There's Devonte Adams, Blue Wave. Right, Kirk's with the Jags. So does Rondale Moore get some more looks? Cadarius, Tony to 175. I think Zach, Matt thinks Zach Wilson will still end up being the best in this class by the time all said and done. Is that Cunningham to 225? Also likes Davis Mills for the Texans. Speaking of the Texans, this card goes to Steven Flatt. Yeah, I mean, I thought the Texans would be, would make a move for a QB, but I guess they were comfortable with the way Davis Mills finished off the season. There's Alan Robinson to 249. Got some Najee Harris right here. Steelers, that'll be for Steven Flatt. Jaylen Ramsey, Blue Cracked Ice, one out of 99. Aaron with the Rams. What about Trey Lance? There's Nick Bolton to 199. Chiefs. There'll be for Ryan. Trey Lance base, Michael Robinson in the Niners. Yeah, with all that coaching staff drama for the Jaguars, I feel like you just have to delete Trevor Lawrence's first year. Calvin Cook to 125. Jaylen Hertz to 175. Well, Logan's way too early Super Bowl prediction is Packers and Chargers. Who's Aaron Rodgers gonna throw it to? Jaylen Hertz goes to the Eagles, Michael Robinson. Jimmy has the Vikings. Jerome Betis to 249. The bus going to Steven Flatt and the Steelers. Brian's got a bold prediction here. In 10 years, he sees the following. Trevor Lawrence number one, Trey Lance two, Matt Jones three. There's Marquette Stevenson. And the last auto is Brian Sight. Old Browns quarterback, Cleveland. This is for you.  And we'll do a recap, an autograph recap at the end as well. All right, next box. I like that, Mark. Raiders and Carl surprised everyone in his opinion. Put 100 bucks on car for MVP at plus, at plus 3,300, 33 to one. I don't think Brian's saying that Trevor Lawrence is gonna be a number one quarterback, I think of this class. I think of this class, I think he's saying that Trevor Lawrence will be the best amongst that draft class. Right, Brian? Or you're not saying he's gonna be a number one quarterback in 10 years, right? I think it'd be good for the hobby, Brian, if he has a pretty good NFL career. Kyle Tras to 225. Juju Smith's choose term. Trask, marinating behind Brady. Jose with the Buccaneers. Yeah, Brian's bullish on Trevor Lawrence. Cam is prospect, needs some good weapons like all QBs do. Look at Peyton's first year. Look at subsequent years. The thing with Peyton Manning though, weren't the Colts just a better run organization? I don't know, some people, there's maybe question marks about Jags ownership though. There's Dante Hall for the Chiefs. The return of Coach Karts? There's Rex Ryan for the Ravens. Givante Williams red wave to 149. Right, and that's kind of where I'm leaning with Mark here, where I don't doubt the physical talents of Trevor Lawrence, but does he have the organization that'll do right by him? There's Amon Green to 49. There's Bobby Wagner to 175. Jimmy Graham to 225. Marcus May to 199. And Amon Ross St. Brown.  Marcus May to 199. Quinn and Williams to 225. Yeah, I agree with you, Brian. That's just the big question mark. And I think we all agree on this, will the organization do right by him? I think Doug Peterson's a solid coach. I think that's a good start, you know? But yeah, Christian Kirk for 20 million. I mean, maybe they didn't really have any other options, but we'll see how that works out. We'll see how future drafts work out. We'll see how this year's draft picks work out. They've got a ways to go, but hey, I'm rooting for Trevor Lawrence. That's gonna be good. He's gonna be good for the hobby. That's Colts edition of Rock Yaw Sin. That's gonna be for Jeremy. He's with the Raiders now. Raven Jordan to 249. And Van Jefferson. Rams, last spot mojo. Aaron, trendsetter with the Rams. Josh Allen, red wave to 149. Right, Brian's like, hey, Trevor Lawrence isn't Bo Callahan. That's all I'm saying. I did hear about that Sean D. Who's saying, did you see the LeBron triple logo man going up for auction? Auction and people are saying $6 million, possibly? It's wild. Do you think it actually gets to $6 million? When we were first doing those Panini flawless breaks, we were thinking a million. But to hear six seems pretty wild. Oh, nice Brian, congrats from the personal break side, right? That's awesome, congrats on that. That's awesome. You know that very day I pulled the Mahomes version of that set too. So we got a little lucky there. Oh, Drake will just outbid everybody. He'll raise the prices. Oh, when does that auction start? Sean, I wonder, I'll have to keep, well, I certainly have to keep track of it. What do you think that Brady's gonna go for, Brian? I think we were kind of speculating about that too. Put a bid on the LeBron, it'll out of my price range. Yeah, I think it's golden as well. I'll bid 100 bucks. If it's PSA 10, pop one, 50,000, that'd be nice. It was my guy Darren Waller, 32 out of 225. We're just talking about him Trevor Lawrence. You can almost, last season probably a wash with all the coaching staff drama, but maybe this year will be different. He's got his buddy Travis Etienne. There's Trey Nixon and Matt Ryan, sensational signature, still a Falcon in this edition. 17 out of 25. ATL, John, got the Falcons in that team right at random. Brian, you don't have to do that. Trust me, there'll be a lot of times where we're not pulling you monsters like that, so we'll be doing group breaks and not getting things. That's your tip to us. Trey Nixon to 175, Patriots, that'll be Tyler. To 249, there's Chris Herndon, fourth. Jets, that'll be for Barry. Kenneth Gainwell purple to 125, Vonte Maddox. Is that right, Mike? Dan Marino to 99. Could the Falcons just not afford Matt Ryan, or did he just want to leave? Well, I think they can afford him, they already paid him. I think he just kind of, you know, I think they were rebuilding. I think maybe they did him a solid by letting him go to a more competitive team. AJ Brown to 149, Hunter Long Silver. I don't think there's really, they're rebuilding and paying him a lot of money. Maybe they thought they could allocate some resources elsewhere. I think both sides kind of, yeah, it's time to move on. I think both sides are ready to move on. There's Mike Allsot to 60, and Rashad Bateman for the Ravens. Does he get more looks now that Mark Keese Brown isn't there? There's more targets. 23 out of 25. Aaron with the Ravens. There's Joe Sherbert, Jags. It's Sean Maddock with the Jaguars. Right, and Mark Andrews, big up tick on targets. There's some height, Jonathan Taylor, out of 10. Nice low number here for the blue horseshoes. Jeremy with the Colts. There's Jamie Newman, 96 out of 199 for the Eagles. That'll be for Michael. And the Eagles, kid reporter card. There's Tommy Trembl, that's a catch. Look at that, hands out in front, eyes locked in on the ball. That's the way to do it, kids. There's 225, James White. DeMarcus Lawrence, orange, 249. And, ooh, look at that. Trade Lance, color blast. And that's for Michael Robinson, who won a team random spot in the prestige filler box, then got randomized the Niners. Ends up with the Trade Lance. There you go, and a Zach Wilson out of here too for Barry and the Jets. Yeah, and they called a color blast earlier. You're welcome, man. I don't know, maybe there's a second, Brian. Someone was telling me a story yesterday about how they saw a box of Crown Royale that had like four kabooms in there, something like that, so maybe there'll be one of those, like in Monopoly, a bank error in our favor. Ah, so the color blast, similar to the manga odds, one in every 12 cases or 14 cases, as the case may be. Got Cam Newton Orange, 249 for the Patriots. Kenneth Gainwell, 225. Trevor Lawrence, base rookie card right on top. Sean Maddock with that one. Anthony's hopeful of a manga on the other side, that'd be pretty amazing. It's Kaleas Campbell to 60. It's Kurt Warner to 149, and a Jamar Chase rookie silver. That's Han with the bangles. Hopefully he keeps it up next year. They did improve that offensive line, at least on paper. And if it works in practice, that's gonna be a very good offensive team. There's Devin White to 225. Cardinals, Kurt Warner, Red Wave going to Ryan, by the way. That is out of 149. Kaleas Campbell, Orange Wave to 60. Ravens, Aaron Billingsley. There's Deyo, Ode Bingo, and there's Ed Reid, flashback autograph for Aaron and the Purple Birds. 25 out of 49 on that Ed Reid. Deyo, 225. That'll be for Jeremy and the Colts. Keenan Allen, Orange to 249 for the Bolts. That's gonna be for Anthony and the Chargers. And a Justin Fields. Wow, I pulled one in a completely different break from a different case. And here's another one. Stephen Flatt with Chicago Bears, won that spot in a filler, got randomized the Bears and the team random, ends up with the Justin Fields autograph. Nice. And the color blast in this box. Woo. Jordan Brooks goes to the Seahawks. That's gonna be for Kevin. Zach Wilson, Mark Brinell to 175. Sean and the Jaguars. Zach Wilson for the Jets, Barry David. Sam Allinger to 199 for the Colts. Jordan Love and DeSean Watson, Silver to 225. All right, two boxes to go. Remember, the second half of this picker team is right over there. jaskyscasebreaks.com, if you wanna run this back. It looks like picker team eight is already in a filler. So it looks like some full spots in a team random and a filler for the team. So exactly the way we did picker team seven. It looks like there's only one filler we gotta do. That's exactly, that's what the schedule says, Tyler. So it must be true. Obviously picker team eight's not sold out yet. So by the powers of deduction, picker team seven. You have a team in this? How you do? I don't think we've seen that guy yet. We've got two boxes to go though. It's a little more slippery, little more slippery-er than previous years. Fields Denzel Ward, blue ice to 99. See how Justin Fields does this here, see him with the bears. Out of 149, Aaron Jones, there's Derek Carr. Mark was saying earlier he put a little down on Derek Carr's futures. I hope he's right as a Raiders hand. The Raiders, the silver and black, Jeffrey. Got my Raiders straight up, gets the Derek Carr autograph. Nice. DK Metcalf, to 175. Went to a Raiders Broncos game last season. Now what a, what a great stadium. Seth Williams to 199. That'll be for my rivals, the Broncos. That'll be for Shawn Matic. Pat Friarmuth, his teammate TJ Watt to 199. Centering a little off on that. Pittsburgh, that's for Stephen Flatt. Stephen, you'll get that Friarmuth too. Moot, moot, and there's Taysom Hill. You might get some looks, right? 229. Oh geez, Matt, I forgot to turn back to that game. Watching the baseball game right now. So the Oilers were up, and now Matt Lieman saying it's 4-4 in that As Oilers game. Oilers trying to avoid that sweep. Avoid the broomsticks. 44 out of 49, Terry McLauren. Greg, and the commanders. That's gotta, this guy's gotta be a big help for Trevor Lawrence, right? Travis Etienne Jr., his former teammate. It's Kyler Murray to 249. Khalil Herbert and Amir Smith-Marcet. Red Wave autograph for the Vikings. Jimmy got the Vikings straight up, thanks for that. 16 out of 149, Skoll. And Khalil Herbert Red Wave will go to Chicago, Shaitown to 149. Yeah, might be time to dust off those broomsticks. Might have to, might have to get those brooms from the Quidditch broom closet at Hogwarts. That's Devonta Smith to 99. That's for Michael Robinson. Call Harry up, we need some brooms. Someone send an owl to Harry Potter. 39 out of 199, Bobby Wagner. Kenneth Murray to 225. And a Remandry Stevenson rookie silver for Tyler. And the Pat Riots. All right, and the final box, ladies and gentlemen. Same break you were watching before, Brian. We're down to our final box. And we got a schedule too. If you click that schedule, you'll always know what we're doing, what we've done, and what we're gonna do. If you click the link in the chat by nightbot or if you click the link that's pinned in the chat, always have access to that spreadsheet 24 hours a day. And Eddie's saying, yes, there are Brock Lesnar autos in this. Is he assigned to a team, Eddie? Do you know? Or will that be randomized to one person in the entire group? It's a Viking edition. I know nothing about Brock Lesnar. Is he from Minnesota? Is that why? Or somehow, or is just a big Vikings fan? I mean, I know who he is. I don't know much about him. There's Jordan Brooks and Debo. Debo Samuel. Where does Debo Samuel end up? Oh, an old training camp photo. Used to, got it, okay. That's pretty cool. Debo Samuel for the Niners. Michael Robinson. He was briefly with the Vikings. Jalen Waddle rookie card of Von Miller to 175 and a DK Metcalf to 49. Where does he end up? Von Miller apparently running a nice little Pass Rush Academy that Max Crosby and Chase Edmund was at. There's Jay Tuffle, 25 for the Jaguars. It's a cool camo pattern in the background. Jaguar, Sean Maddock. Blake Martinez to 149. Got Chas Serrat. And wow, look at this. A three color patch auto, Justin Fields. And that's another Justin Field auto for Stephen Flatt and the Chicago Bears. I really hope he does well next season. I'm rooting for him. 32 out of 99. Nice. And there's an Oilers goal and now it's 5-5. Speaking of the Vikings, there's Chas Serrat. We've got Jordan Lewis, 55 out of 249. Denzel Mims to 175. That'll be for Barry and the Jets. Antonio Gates to 249. Did you know that Antonio Gates used to play basketball? I feel like every broadcast says that like for the entirety of his career would say that. We're like, yes, yes, we know. We know. We've told us the first seven years of his career. Joe Montana to 225. Sean Taylor, Jalen Phillips to 225. Mark Andrew Silver. We got Daniel Jones. I hope he does well this season. 9 out of 15. That'd be good for the hobby. Daniel Jones to 15. New York football Giants, the G-Men. Big Blue. Eddie with the Giants. Got some Kyle Trass. Marvin Jones, Jr. to 125. And a Trey Sermon Silver for the Niners. I think Elijah Mitchell ended up being the guy that emerged there, but maybe Trey Sermon can show us something too this year. Maybe there's some injuries, I forget. All right, there you go, ladies and gentlemen. That was 2021 Panini Prison Football 6-Box half case picker team number seven from jaskiescasebrakes.com. Really solid stuff. More in the store on the website. Check it out. There's a quick little recap here. Justin Fields autographed, Jamar Chase. Silver, Trevor Lawrence cards at Jonathan Taylor hype. What's the 10? Van Jefferson, Amonra St. Brown. And a Trey Lant color blast and a Justin Fields RPA. That's pretty awesome. There you go, ladies and gentlemen. I'm Joe for jaskiescasebrakes.com. Thanks for watching. Thanks for breaking with us. And I'll see you next time for the next one. Bye-bye.