Chapter 4 - Exponential and Logarithmic Functions - Section 4.5 Properties of Logarithms - 4.5 Assess Your Understanding - Page 332: 76

$2.584$

Change of Base Formula: $\hspace{20pt} \log_ a M = \dfrac{\log_b M}{\log_b a}$ $\log_{\sqrt{5}} 8= \dfrac{\log_{10} 8}{\log_{10} \sqrt{5}}$ Where: $a=\sqrt{5} \hspace{10pt} M = 8 \hspace{10pt} b = 10$ $ \dfrac{\log_{10} 8}{\log_{10} \sqrt{5}} \approx \boxed{2.584}$