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Chapter 12: Problem 68

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

Short Answer

Expert verified
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 by step solution

01

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.
02

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.
03

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.

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Most popular questions from this chapter

The loudness level of a sound, \(D,\) in decibels, is given by the formula $$D=10 \log \left(10^{12} I\right)$$ where I is the intensity of the sound, in watts per meter \(^{2} .\) Decibel levels range from \(0,\) a barely audible sound, to \(160,\) a sound resulting in a nuptured eardrum. Use the formula to solve Exercises. The sound of a blue whale can be heard 500 miles away, reaching an intensity of \(6.3 \times 10^{6}\) watts per meter? Determine the decibel level of this sound. At close range, can the sound of a blue whale rupture the human eardrum?

a. Evaluate: \(\log _{2} 16\) b. Evaluate: \(\log _{2} 32-\log _{2} 2\) c. What can you conclude about $$\log _{2} 16, \text { or } \log _{2}\left(\frac{32}{2}\right) ?$$

Explain how to find the domain of a logarithmic function.

Solve each equation in Exercises \(144-146 .\) Check each proposed solution by direct substitution or with a graphing utility. $$\ln (\ln x)=0$$

Solve each equation. $$5^{2 x} \cdot 5^{4 x}=125$$
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