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Naperien logarithm

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

 


Explanation

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 a logarithm is the inverse of an exponential function, because

en = x  has the inverse  n = ln x

A logarithmic function itself describes a "stray" exponent.

 


Example 1

From the definition follows

eln (7) = 7

as ln (7) = 1.945910149 and so

e1.945910149 = 7

 


Additional information

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

 


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