Answer
$\dfrac{3}{4}$
Work Step by Step
Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $
\log_{16}8
,$ is equivalent to
\begin{array}{l}\require{cancel}
\log_{16}\left(\sqrt[4]{16}\right)^3
\\\\=
\log_{16}16^{3/4}
\\\\=
\dfrac{3}{4}\log_{16}16
.\end{array}
Since $\log_bb=1,$ the expression, $
\log_{16}16
,$ simplifies to $1$.
\begin{array}{l}\require{cancel}
\dfrac{3}{4}(1)
\\\\=
\dfrac{3}{4}
.\end{array}