Answer
$x=1+\ln{16}\approx 3.7726$
Work Step by Step
\begin{align*}
e^{x-1}&=16 &\text{Divide 4 to both sides.}\\\\
\ln{e^{x-1}}&=\ln{16} &\text{Take the natural logarithm of both sides.}\\\\
(x-1)(\ln{e})&=\ln{16}&\text{Power Property of Logarithms.}\\\\
(x-1)(1)&=\ln{16}&\text{Note that $\ln{e}=1$.}\\\\
x-1&=\ln{16}\\\\
x&=1+\ln{16}&\text{Add 1 to both sides.}\\\\
x&\approx 3.7726\end{align*}
Check:
\begin{align*}
4e^{1+\ln{16}-1}&\stackrel{?}=64\\\\
4(16)&\stackrel{\checkmark}=64\end{align*}
Thus, the solution is $x=1+\ln{16}\approx 3.7726$.
