Answer
$x=\dfrac{\pi}{2}$
Work Step by Step
Using the properties of logarithms, the given equation, $
\ln e^{2x}=\pi
$ is equivalent to
\begin{align*}\require{cancel}
2x\ln e&=\pi
&(\text{use }\log_b x^y=y\log_b x)
\\
2x(1)&=\pi
&(\text{use }\ln e=1)
\\
2x&=\pi
\\\\
\dfrac{\cancel2x}{\cancel2}&=\dfrac{\pi}{2}
\\\\
x&=\dfrac{\pi}{2}
.\end{align*}
Hence, the solution to the equation $
\ln e^{2x}=\pi
$ is $
x=\dfrac{\pi}{2}
$.
