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Inverse of the exponential function

The inverse of the exponential function ex is the natural logarithm ln x.

 


Explanation

We take the exponential function

ex = a

To determine the inverse function we have to answer the question: To what power do I have to raise the base e to find a? The answer is

to the power   loga

It is nothing but a number. The spelling frightens everyone in the beginning. Let's get over it quickly, so that

x = ln a.

A logarithm is the inverse of an exponential function.

Shown here are ex (red) and ln x (green).

 


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