# What is ln(e^x)?

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Gió Share
Nov 11, 2015

#### Answer:

It is exactly $x$.

#### Explanation:

You are looking for a number that is the exponent of the base of $\ln$ which gives us the integrand, ${e}^{x}$;
so:
the base of $\ln$ is $e$;
the number you need to be the exponent of this base to get ${e}^{x}$ is.....exactly $x$!!!
so:
$\ln \left({e}^{x}\right) = {\log}_{e} \left({e}^{x}\right) = x$

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