# How do you use the Change of Base Formula and a calculator to evaluate log_pi (sqrt{2})?

${\log}_{b} a = \log \frac{a}{\log} b = \ln \frac{a}{\ln} b$
${\log}_{\pi} \sqrt{2} = \ln {2}^{\text{1/2}} / \left(\ln \pi\right) = \frac{\frac{1}{2} \ln 2}{\ln} \pi = \ln \frac{2}{2 \ln \pi}$