Answer
The solution set is $\left\{ \frac{\ln 4}{3} \right\}$ which equals to $0.46$.
Work Step by Step
Let us consider the following equation.
$\begin{align}
& 9{{e}^{3x}}-4=32 \\
& 9{{e}^{3x}}=32+4 \\
& 9{{e}^{3x}}=36 \\
& {{e}^{3x}}=\frac{36}{9}
\end{align}$
Solving further,
${{e}^{3x}}=4$
Take the natural logarithm on both sides.
$\begin{align}
& 3x=\ln 4 \\
& 3x=1.386 \\
& x=\frac{1.386}{3} \\
& =0.46
\end{align}$
