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Common logarithm

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

10^log x = x

 

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Explanation

We start with the exponential function

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

10^log 1 = 1
10^log 2 = 2
10^log 3 = 3
10^log 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

 

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Example 1

It follows from the definition

10^log (7) = 7

because log (7) = 0.84509804 and so

10^0,84509804 = 7

 

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Example 2

By thinking carefully, you can find the solution of

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

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

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

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

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

where this answer is accurate to three decimal places.

 

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

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