Answer
$e^{-1}=\frac{1}{e}$
Work Step by Step
We know that if $b\gt0$ and $b\ne1$, then $y=log_{b}x$ is equivalent to $x=b^{y}$ (where $x\gt0$ and $y$ is a real number).
Therefore, $log_{e}\frac{1}{e}=-1$ can be written as the exponential equation $e^{-1}=\frac{1}{e}$.