Use the change-of-base formula and a calculator to evaluate the following logarithm. \( \log _{\pi} 71 \)

To evaluate \( \log_{\pi} 71 \) using the change-of-base formula, follow these steps: ### **Step 1: Apply the Change-of-Base Formula** The change-of-base formula allows us to compute logarithms with any base using natural logarithms (base \( e \)) or common logarithms (base \( 10 \)). The formula is: \[ \log_{a} b = \frac{\ln b}{\ln a} \] For \( \log_{\pi} 71 \), this becomes: \[ \log_{\pi} 71 = \frac{\ln 71}{\ln \pi} \] ### **Step 2: Calculate the Natural Logarithms** Using a calculator, find the natural logarithms of 71 and \( \pi \): \[ \ln 71 \approx 4.262680526 \] \[ \ln \pi \approx 1.144222766 \] ### **Step 3: Divide the Results** Now, divide the two logarithmic values: \[ \log_{\pi} 71 = \frac{4.262680526}{1.144222766} \approx 3.7245 \] ### **Final Answer** \[ \log_{\pi} 71 \approx 3.7245 \]