Question

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

${\log }_{\frac{1}{3}}71$

Short answer

$-3.880$

Step-by-step solution

Step 1. Given information.

Consider the given information.

${\log }_{\frac{1}{3}}71$

Step 2. Calculation.

Apply the base change formula to simplify.

$\begin{array}{rcl}{\log }_{\frac{1}{3}}71& =& \frac{\log 71}{\log \frac{1}{3}}\\ & =& \frac{\log 71}{\log 1-\log 3}\\ & =& \frac{\log 71}{0-\log 3}\\ & =& \frac{\log 71}{-\log 3}\\ & \approx & -3.880\end{array}$