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Chapter 3: Problem 72

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$\log _{6} 17$$

Short Answer

Expert verified
The logarithm \( \log _{6} 17 \) to four decimal places is 1.7712.

Step by step solution

01

Apply the Change of Base Formula

First, apply the change of base formula to \( \log _{6} 17 \). This can be done with either common logarithms or natural logarithms. By definition, the change of base formula is: \( \log _{b} a = \frac{\log _{p} a}{\log _{p} b} \). Following this formula, we will rewrite the expression: \( \log _{6} 17 = \frac{\log _{10} 17}{\log _{10} 6} \) or \( \log _{6} 17 = \frac{\ln 17}{\ln 6} \)
02

Use a Calculator

Next, use a calculator to find the values to four decimal places. If using common logarithms (base 10), calculate \( \log _{10} 17 \) and \( \log _{10} 6 \). If using natural logarithms (base e), calculate \( \ln 17 \) and \( \ln 6 \).
03

Complete the Division

Finally, divide the values you obtained from the calculator. Make sure to divide the logarithm of the original number by the logarithm of the original base (in this case, 17 is divided by 6).

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