## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

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