Question

Use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places.

${\log }_{\pi }\sqrt{2}$

Short answer

$0.303$

Step-by-step solution

Step 1. Given information.

Consider the given information.

${\log }_{\pi }\sqrt{2}$

Step 2. Calculation.

Apply the base change formula and simplify.

$\begin{array}{l}{\log }_{\pi }\sqrt{2}=\frac{\log \sqrt{2}}{\log \pi }\\ =\frac{1}{2}\left(\frac{\log 2}{\log \pi }\right)\\ =\frac{0.605}{2}\\ \approx 0.303\end{array}$