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Chapter 12: Problem 62

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

Short Answer

Expert verified
The value of \(\log _{6} 17\) to four decimal places can be calculated by evaluating \(\frac{{\log 17}}{{\log 6}}\) or \(\frac{{\ln 17}}{{\ln 6}}\) with a calculator and then rounding the result.

Step by step solution

01

Change of base

A logarithm with any base can be calculated by change of base. Use the formula: \[\log_b a = \frac{{\log a}}{{\log b}}\] So, the given logarithm \(\log _{6} 17\) can be expressed as \[\log _{6} 17 = \frac{{\log 17}}{{\log 6}}\] or \[\log _{6} 17 = \frac{{\ln 17}}{{\ln 6}}\] where \(\log\) means base-10 logarithm and \(\ln\) means natural logarithm (base e).
02

Calculate the new logarithms

Now use a calculator to estimate these new logarithms. Plug in the numbers and calculate. Remember to keep at least four decimal places in your calculations.
03

Round the results

Once you have calculated the new logarithm, round the number to four decimal places as asked by the exercise.

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Most popular questions from this chapter

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