<    1      2      3      4      5    >

### Common logarithm

A common logarithm is the exponent of an exponential function with base 10

10log x = x

##### Explanation

10n = x

and want to calculate n. So we must answer the question: To which power do we have to raise the base 10, to get x ? The answer is

to the power   log x

So applies

10log 1 = 1
10log 2 = 2
10log 3 = 3
10log 4 = 4

The spelling scares everyone off in the beginning. Let's just remember that a logarithm is the inverse of an exponential function, because

10n = x  has the inverse  n = log x

##### Example 1

It follows from the definition

10log (7) = 7

because log (7) = 0.84509804 and so

100,84509804 = 7

##### Example 2

By thinking carefully, you can find the solution of

10x = 1000     ⇒     x = log (1000) = 3

10x = 1           ⇒     x = log (1) = 0

10x = 0.1         ⇒     x = log (0.1) = −1

On a calculator you can find the value x = 1.892… for

10x = 78         ⇒     x = log (78) = 1.892

where this answer is accurate to three decimal places.

##### History

English mathematician Henry Briggs (1561 - 1630) gained fame for his development and dissemination of logarithms.