Answer
$9$
Work Step by Step
Using $\log_bx^m=m\log_bx$ or the Power Rule of Logarithms, the given expression, $
\log_{6}6^9
,$ is equivalent to
\begin{array}{l}\require{cancel}
9\log_{6}6
.\end{array}
Since $\log_bb=1,$ the expression, $
\log_{6}6
,$ simplifies to $1$.
\begin{array}{l}\require{cancel}
9(1)
\\\\=
9
.\end{array}