Answer
$4$
Work Step by Step
Let $
x=e^{\ln4}
$. Taking the natural logarithm of both sides results to
\begin{align*}\require{cancel}
\ln x&=\ln e^{\ln4}
.\end{align*}
Using the properties of logarithms, the equation above is equivalent to
\begin{align*}\require{cancel}
\ln x&=(\ln4)(\ln e)
&(\text{use }\log_b x^y=y\log_b x)
\\
\ln x&=(\ln4)(1)
&(\text{use }\ln e=\log_e e=1)
\\
\ln x&=\ln4
.\end{align*}
Since $\ln x=\ln y$ implies $x=y$, then the equation above implies
\begin{align*}
x&=4
.\end{align*}
With $x=e^{\ln4}$ and $x=4$, then $
e^{\ln4}
$ evaluates to $
4
$.
