Algebra Tutorials!
Wednesday 8th of July
Solving Linear Equations
Systems of Linear Equations
Solving Linear Equations Graphically
Algebra Expressions
Evaluating Expressions and Solving Equations
Fraction rules
Factoring Quadratic Trinomials
Multiplying and Dividing Fractions
Dividing Decimals by Whole Numbers
Adding and Subtracting Radicals
Subtracting Fractions
Factoring Polynomials by Grouping
Slopes of Perpendicular Lines
Linear Equations
Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
Writing Linear Equations Using Slope and Point
Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
Solving Equations 3
Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
Rounding Numbers
Factoring by Grouping
Polar Form of a Complex Number
Solving Quadratic Equations
Simplifying Complex Fractions
Common Logs
Operations on Signed Numbers
Multiplying Fractions in General
Dividing Polynomials
Higher Degrees and Variable Exponents
Solving Quadratic Inequalities with a Sign Graph
Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
Solving Linear Equations
The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
Rotating an Ellipse
Multiplying Numbers
Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
Straight Lines
Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines
Try the Free Math Solver or Scroll down to Tutorials!












Please use this form if you would like
to have this math solver on your website,
free of charge.

Common Logs

Notation for Common Logs

A logarithm has the form logbx, where x and b are real numbers, x > 0, b > 0, and b 1.

A common logarithm has 10 for its base, b. Here are several examples of common logs:

log 10 1000 log 10 43 log 10 0.87

Common logs are often abbreviated by not writing the base.

For example, the common logarithms shown above can be written as:

log 1000 log 43 log 0.87


Definition â€” Common Logarithm

A common log is a log whose base is 10. It is written like this:

log x = log10 x Here, x > 0.

Common logs are useful since they have the same base as our number system, which is base 10.


Finding Common Logs

We can find the value of some common logs by switching from logarithmic notation to exponential notation.


Example 1

Find: log 10,000


The base of a common log is 10.

Therefore, write log 10,000 as log10 10,000.

Set x equal to log10 10,000.

Rewrite in exponential form.

Rewrite 10,000 as a power of 10.

Use the Principle of Exponential Equality to solve for x.

So, log 10,000 = 4.



x =

10x =

10x =

x =


log10 10,000

log10 10,000





A factor tree can be used to write 10,000 as a power of 10.

Thus, 10,000 = 10 Â· 10 Â· 10 Â· 10 = 104.

Principle of Exponential Equality:

If bx = by, then x = y. Here, b > 0 and b 1.


In many cases we cannot find the value of a common log by switching from logarithmic notation to exponential notation.

For example, we can rewrite x = log 65 as 10x = 65, but it isnâ€™t easy to see what power of 10 equals 65.

We can approximate log 65 by noting the following:

1 = log10 10 is equivalent to 101 = 10

x = log10 65 is equivalent to 10x = 65

2 = log10 100 is equivalent to 102 = 100

So, log 65 must be between 1 and 2.

Copyrights © 2005-2020