Answer
$x=\dfrac{1}{e^2}$
Work Step by Step
Recall:
$$\ln{a}=y \longleftrightarrow e^y=a$$
Use the definition above to obtain:
\begin{align*}
\ln{x}&=-2\\\\
e^{-2}&=x\\\\
\end{align*}
Use the rule $a^{-m} = \dfrac{1}{a^m}$ to obtain:
$$\dfrac{1}{e^2}=x$$
