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Common logarithm

A logarithm is the exponent of an exponential function

x = 10log x

 


Explanation

We start with the exponential function

x = 10n

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

to the power   log x

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

 


Examples

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

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

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

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

 


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