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Logarithmic exponent

An antilogarithm describes an exponential function where the exponent is a logarithm

e ln x = x



We take the exponential function

e n = x

and want to calculate n. So we must answer the question: To what power do we 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.


Example 1

From the definition of the logarithm follows that you can write each number as an exponential function, so

1 = eln (1)

And because ln (1) = 0 you get

1 = eln (1) = e0 = 1

The zeroth power always delivers the value 1.


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