Answer
$x = \frac{1}{2}$
Work Step by Step
Let
$\log_{81}{9} = x$
RECALL:
$\log_b{y} =x \longrightarrow b^x=y$
Use the rule above, where $y=9$ and $b=81$, to obtain:
$81^x=9^{1}$
Write 81 as $9^2$ to obtain:
$(9^2)^x=9^{1}
\\9^{2x} = 9^{1}$
Use the rule "If $a^x=a^y$, then $x=y$" to obtain:
$2x=1
\\x = \frac{1}{2}$