# Common Logarithm of a Number

## Common Logarithm of a Number

Exponent to which the number 10 must be raised to obtain a given number.

• Consider the expression $$\log_{10}(649) ≈ 2.812$$.
The characteristic (the integer part of the logarithm) is 2, and the mantissa is 0.812, or 2.812 – 2 = 0.812.
• Consider the expression $$\log_{10}(3.779) ≈ 0.577$$.
The characteristic (the integer part of the logarithm) is 0, and the mantissa is 0.577, or 0.577 – 0 = 0.577.

### Notation

If $$a$$ = 10$$^{n}$$, then $$n$$ is the common logarithm of $$a$$ to the base 10.

This relationship is written as: $$n = \log_{10}(a)$$ which is read as “$$n$$ is equal to the logarithm of $$a$$ to the base 10″.

### Examples

• If log$$_{10}(100) = 2$$, then 100 = 10$$^{2}$$.
• If log$$_{10}(1000) = 3$$, then 1000 = 10$$^{3}$$.