Answer
$\dfrac{5}{2}$
Work Step by Step
Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $
\log_{4}32
,$ is equivalent to
\begin{array}{l}\require{cancel}
\log_{4}\left(\sqrt{4}\right)^5
\\\\=
\log_{4}4^{5/2}
\\\\=
\dfrac{5}{2}\log_{4}4
.\end{array}
Since $\log_bb=1,$ the expression, $
\log_{4}4
,$ simplifies to $1$.
\begin{array}{l}\require{cancel}
\dfrac{5}{2}(1)
\\\\=
\dfrac{5}{2}
.\end{array}