Answer
$x=-\pi$
Work Step by Step
Using the properties of logarithms, the given equation, $
\ln e^{-x}=\pi
$ is equivalent to
\begin{align*}\require{cancel}
(-x)\ln e&=\pi
&(\text{use }\log_b x^y=y\log_b x)
\\
(-x)(1)&=\pi
&(\text{use }\ln e=1)
\\
-x&=\pi
\\
x&=-\pi
.\end{align*}
Hence, the solution to the equation $
\ln e^{-x}=\pi
$ is $
x=-\pi
$.
