Answer
The solution set is $\left( 67 \right)$
Work Step by Step
${{\log }_{4}}\left( {{x}^{2}}-9 \right)-{{\log }_{4}}\left( x+3 \right)-{{\log }_{4}}64=0$
So,
$\begin{align}
& {{\log }_{4}}\left( \frac{{{x}^{2}}-9}{x+3} \right)={{\log }_{4}}64 \\
& \frac{{{x}^{2}}-9}{x+3}=64 \\
& {{x}^{2}}-9=64\left( x+3 \right) \\
& {{x}^{2}}-9=64x+192
\end{align}$
$\begin{align}
& {{x}^{2}}-64x+201=0 \\
& \left( x-67 \right)\left( x+3 \right)=0 \\
& x-67=0,x+3=0 \\
& x=67,x=-3
\end{align}$
We reject the solution $x=-3$ because it requires us to take the log of $0$, which is undefined.
Hence, the solution set is $\left( 67 \right)$
