Answer
$x=\frac{1}{2}$
Work Step by Step
First, we let
$\log_{6}{\sqrt6} = x$
RECALL:
$\log_b{y} =x \longrightarrow b^x=y$
Use the rule above, where $y=\sqrt6$ and $b=6$, to obtain:
$6^x=\sqrt6$
Write $\sqrt6$ as $ 6^{\frac{1}{2}}$ to obtain:
$6^x=6^{\frac{1}{2}}$
Use the rule "If $a^x=a^y$, then $x=y$" to obtain:
$x=\frac{1}{2}$