Answer
$\left\{3\right\}$
Work Step by Step
Using the properties of logarithms, the given equation, $
\ln e^x=3
,$ is equivalent to
\begin{align*}\require{cancel}
x\ln e&=3
&(\text{use }\log_b x^y=y\log_b x)
\\
x(1)&=3
&(\text{use }\ln e=1)
\\
x&=3
.\end{align*}
Hence, the solution set of the equation $
\ln e^x=3
$ is $
\left\{3\right\}
$.
