# How do I find the inverse of e^x?

Sep 5, 2014

The answer is $y = \ln x$.

We find the answer the same way we find any inverse; we swap $x$ and $y$ then solve.

$y = {e}^{x}$
$x = {e}^{y}$ swap
$\ln x = \ln \left({e}^{y}\right)$ take logarithm of both sides
$\ln x = y$

$\ln$ and $e$ functions cancel each other because they are inverses.