Chapter 4 - Exponential and Logarithmic Functions - Section 4.5 Properties of Logarithms - 4.5 Assess Your Understanding - Page 332: 78

$0.303$

Change of Base Formula: $\hspace{20pt} \log_ a M = \dfrac{\log_b M}{\log_b a}$ $\log_{\pi} \sqrt{2}= \dfrac{\log_{10} \sqrt{2}}{\log_{10} \pi}$ Where: $a=\pi \hspace{10pt} M = \sqrt{2} \hspace{10pt} b = 10$ $ \dfrac{\log_{10} \sqrt{2}}{\log_{10} \pi} \approx \boxed{0.303}$