Problem 68 - Introductory and Intermediate Algebra for College Students 4th

Question

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$\log _{\pi} 400$$

Step-by-Step Solution

Answer

The value of \(\log_{\pi} 400\) to four decimal places is dependent on the calculated values from step 2 and 3. Input the calculated results of the logarithms into the formula from step 1.

Step 1: Apply the change of base formula

Express the logarithm \(\log_{\pi} 400\) using a base that the calculator can handle. Use the change of base formula to rewrite the given expression as \(\log_{\pi} 400 = \frac{\log 400}{\log \pi}\) if using common logarithm or \(\log_{\pi} 400 = \frac{\ln 400}{\ln \pi}\) if using natural logarithm.

Step 2: Evaluate the logarithms

Use the calculator to evaluate each of the logarithms on the right side of the equation from Step 1. Ensure the calculator is set to the correct mode (either common log or natural log) prior to input.

Step 3: Divide the results

After getting the results from the calculator for each logarithm, divide the results as it was formulated in step 1. Ensure that the division is carried out to four decimal places.