Answer
$\displaystyle \{\frac{1}{3},729\}$
Work Step by Step
(*) For the equation to be defined, it must be true that $x \gt 0$
... Substituting $t=\log_{3}x$ , we have
$t^{2}-5t-6=0 \quad $... two factors of $-6$ that add to $-5$...
$(t-6)(t+1)=0$
$\left[\begin{array}{lll}
t=-1 & or & t=6\\
\log_{3}x=-1 & & \log_{3}x=6\\
\log_{3}x=\log_{3}3^{-1} & & \log_{3}x=\log_{3}3^{6}\\
x=1/3 & or & x=729
\end{array}\right]$
both satisfy (*), so the solution set is
$\displaystyle \{\frac{1}{3},729\}$
