Answer
$\approx1.1592$
Work Step by Step
By using the change of base formula we can calculate easily the value of $\log_{\frac{2}{3}}\frac{5}{8}$.
$\log_{\frac{2}{3}}\frac{5}{8}=\frac{\log_{10}\frac{5}{8}}{\log_{10}\frac{2}{3}}\approx1.1592$
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