Naperien logarithm

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The naperien logarithm is defined as the exponent of an exponential function

We start from the exponential function

and want to calculate n. We must answer the question: To what power do I need to raise the base e to get x ? The answer is

to the power ln x

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

eⁿ = x has the inverse n = ln x

A logarithmic function itself describes a "stray" exponent.

Shown here are e^x (red) and ln x (green).

From the definition follows

e^ln (7) = 7

as ln (7) = 1.945910149 and so

e^1.945910149 = 7

In 1614 the Scottish mathematician John Napier published his book Mirifici Logarithmorum Canonis Descriptio.