Sunday, 31 May 2009

Power Law of Logarithm Explained

Logarithm study has a few formulae that are important and key to solving math questions.

By remembering them , you will be in line to solve logarithmic problems and, maybe, fast too.

However, what if you forget them?
Does it mean that you are not able to solve the question regardless of speed?

Do not despair.
As long as you are able to manage the 2 basic laws in logarithm, you are safe.

The product law and the quotient law are must for any students.

Why do I say that?

Let us take the Power Law and do a review.

n log x = log X n

Why is it so? What if you forget this law? Any problem?

These are the very queries any new learners exposed to logarithm will ask.

First allow me to go through the product law of logarithm.
log (XY) = log X + log Y

Here you see that the product of "X" and "Y" in logarithmic operation, becomes a "sum"of the individual logarithms.

4 log Y = log Y + log Y + log Y + log Y (adding up 4 of the log Y)

Using product law, you know that these 4 terms can be combined to log (Y x Y x Y x Y).

log (Y x Y x Y x Y) = log Y4

Now, you see, through the product law, you are able to equate the 4 log Y into log Y4 ,
meaning, 4 log Y = log Y4.

You see that you did not utilise the Power Law here,and yet is able to form this formula!
Amazing isn't it.

What is the message here?
The message is that, when you have the basic understanding in logarithmic principles, you will be able to twist and turn any given problems to come out a solution.

You had used the basic product law to discover this unique Power Law.
It is similar to other laws and also can be expanded to cover other maths topics too.

Do enjoy maths.
Do discover more exciting twists it presents wwith a bit of thinking.

Happy learning :-)


Saturday, 9 May 2009

Learning Math Topics in Isolation

Learning encompasses linking with other area and related topics.

Learning thing with disregard for other is alright for the sake of triggering the mind. But does it benefits more if linked to others?

Does indices related to quadratic equation?
Does multiplication relates to addition?
Does complex number relates to algebra?

All the above questions are common in the mind of a math learners.
If you do not have these questions along the learning phase, something is very wrong.

Learning math in isolation is similar to living in an isolated island all by yourself.
You do not know what is happening in the world.
You do not know if there is famine somewhere, or swine flu going round, or a plane crash near you.

Math has to be done with linkage to many other mathematical topics. It cannot be done in isolation.

Math is a tool that solves real-life problems. With mastery of various mathematical concept and relation among them, you will be better prepare to solve more problems.

Many a time, you will come across students who just study topical math without knowing that they can apply what have been taught to them previously.

They start fresh when a new topic is introduced.
Algebra is different from complex number.
The addition in complex number is done differently from that done in algebra. That's what they assumed, since the heading is different!

Interesting learning ways, right?

That is human nature, to be frank. Only when you are told, sometimes, otherwise you will not know it. Adults learn through experience that this assumption is pulling you down.

The ability to link many things together is a very beneficial skill to permanently internalise.
This does not point to math alone. Others apply.

Math can be tough if learned using an improper learning method.
One good technique is the linking technique where you will see yourself happily doing math, being able to apply and solve questions using previous and current taught concepts.
It motivates you.
This is the STARTING point if you are unaware. This is the point where it decides whether you can sustain math learning.

Learn wide and later deep into math. But start with the correct footing. Link as much to previous as possible. It will be a sure way to happy math doing.

:-) I like math!

Saturday, 2 May 2009

Counting Down With Base Eight

Counting up is an easy task for anyone, even when the base is not ten.

You may refer to this link for counting (up) with base 8.

However, counting down may be slightly harder than normal, especially when dealing with another number base other than 10.

Let's try with base 8 for a start.

03 -

Here a count down of 3 from 10 is needed.

How do you go about it?

Thinking of the way base 10 subtraction was dealt with, this is similar.
After all maths is the same. It is the technique that is important.

When you encounter a " bring back" from the upper (rightmost) digit to the lower leftmost digit, you will, for base 10, add a 10 to the "ones" digit.

Here, with base 8, you will do likewise, except that now it is adding the number 8 to the leftmost digit.

Thus, 0 + 8 = 8.

And 8 - 3 = 5.

03 -
05 (Answer in base 8).

There is nothing difficult if you look at the technique or concept in counting up or down.

Maths is just playing with methods to resolve numerical issues.

The above is a good example. Hope you agree?

Have fun counting in other number base.