Answer
The solution set is $\{\log_{6}3\}$ or $\{0.613\}$
Work Step by Step
... $\quad 36^{x}=(6^{2})^{x}=(6^{x})^{2}$
... Substitute $t=5^{x}$ (t is positive)
... the equation becomes
$t^{2}-6t+9=0 \quad $...recognize a square of a difference
$(t-3)^{2}=0$
$t=3 \quad $... bring back x
$6^{x}=3 \quad $...Apply$: \quad \log_{6}(...)$
$x=\log_{6}3\approx 0.613$
The solution set is $\{\log_{6}3\}$ or $\{0.613\}$
