Answer
$4$
Work Step by Step
Note that $y=\log_a x \text{ is equivalent to } x= a^y$.
Thus, if $y = \log_{\sqrt{3}} 9 \hspace{5pt},$ then $\hspace{5pt}(\sqrt{3})^y=9$
Since $9=3^2=(\sqrt{3})^4$, then
$(\sqrt{3})^y=(\sqrt{3})^4$
Use the rule $a^m=a^n \implies m=n$ to obtain:
$y=4$
Therefore,
$ \log_{\sqrt{3}} 9 = \boxed{4}$
