Question

use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.
evaluate the expression.
\log_{\pi} 47 = \square
(type an integer or a decimal. do not round until the final answer. then round to four decimal places as needed.)

Explanation:

Step1: Use Change of Base Formula

The change of base formula for logarithms is $\log_b a = \frac{\log_c a}{\log_c b}$ (we can use common logarithm with base 10 or natural logarithm with base $e$). Let's use common logarithm (base 10) here. So, $\log_{\pi} 47 = \frac{\log 47}{\log \pi}$.

Step2: Calculate the Logarithms

First, find $\log 47$ and $\log \pi$ using a calculator. $\log 47 \approx 1.672097$, $\log \pi \approx 0.4971499$. Then divide them: $\frac{1.672097}{0.4971499} \approx 3.3634$.

Answer:

3.3634