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Chapter 3: Problem 77

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$\log _{\pi} 63$$

Short Answer

Expert verified
To provide the answer, calculate the values as discussed in step 2 and 3. Use the calculator to get those values.

Step by step solution

01

Apply the Change of Base Formula

Firstly, apply the change of base formula to the given logarithm to make it possible for computation using a calculator. \(\log _{\pi} 63\) can be transformed as \(\log _{\pi} 63 = \frac{\log _{10} 63}{\log _{10} \pi}\) if using common logarithms or \(\frac{\ln 63}{\ln \pi}\) if using natural logarithms.
02

Compute the Logs

Next, calculate both \(\log_{10} 63\) and \(\log_{10} \pi\) if using common logarithm, or calculate \(\ln 63\) and \(\ln \pi\) if using natural logarithm, with the help of a scientific calculator.
03

Compute the Quotient

Finally, divide the result of step 2 to get the answer. That would be the value of \(\log _{\pi} 63\) to four decimal places.

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