Answer
$\dfrac{3}{2}$
Work Step by Step
Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $
\log_{9}27
,$ is equivalent to
\begin{array}{l}\require{cancel}
\log_{9}\left(\sqrt{9}\right)^3
\\\\=
\log_{9}9^{3/2}
\\\\=
\dfrac{3}{2}\log_{9}9
.\end{array}
Since $\log_bb=1,$ the expression, $
\log_{9}9
,$ simplifies to $1$.
\begin{array}{l}\require{cancel}
\dfrac{3}{2}(1)
\\\\=
\dfrac{3}{2}
.\end{array}