Answer
$36$
Work Step by Step
Let $
x=5^{\log_5 36}
$. Taking the logarithm of both sides results to
\begin{align*}\require{cancel}
\log x&=\log5^{\log_5 36}
.\end{align*}
Using the properties of logarithms, the equation above is equivalent to
\begin{align*}\require{cancel}
\log x&=(\log_5 36)(\log5)
&(\text{use }\log_b x^y=y\log_b x)
\\\\
\log x&=\left(\dfrac{\log36}{\log5}\right)(\log5)
&(\text{use Change-of-Base Formula}
\\\\
\log x&=\left(\dfrac{\log36}{\cancel{\log5}}\right)(\cancel{\log5})
\\\\
\log x&=\log36
.\end{align*}
Since $\log_b x=\log_b y$ implies $x=y$, then the equation above implies
\begin{align*}
x&=36
.\end{align*}
With $x=5^{\log_5 36}$ and $x=36$, then $
5^{\log_5 36}
$ evaluates to $
36
$.
