Answer
$5.615$
Work Step by Step
Change of Base Formula: $\hspace{20pt} \log_ a M = \dfrac{\log_b M}{\log_b a}$
$\log_{\sqrt{2}} 7 = \dfrac{\log_{10} 7}{\log_{10} \sqrt{2}}$
Where: $a=\sqrt{2} \hspace{10pt} M = 7 \hspace{10pt} b = 10$
$\dfrac{\log_{10} 7}{\log_{10} \sqrt{2}} \approx \boxed{5.615}$
