Answer
Their error is in the third line $(4x=5)$.
The solution is $x=\frac{e^5}{4}$.
Work Step by Step
The error in the solution is in the third line, which is $4x=5$.
This is because the previous line's right side is $e^5$.
The correct solution is:
\begin{align*}
\ln{4x}&=5\\\\
e^{\ln{4x}}&=e^5\\\\
4x&=e^5\\\\
\frac{4x}{4}&=\frac{e^5}{4}\\\\
x&=\frac{e^5}{4}
\end{align*}
