/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 64 Use common logarithms or natural... [FREE SOLUTION] | 91影视

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Chapter 12: Problem 64

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. $$\log _{16} 57.2$$

Short Answer

Expert verified
The evaluated result of \( \log_{16} 57.2 \) to four decimal places is 1.4591.

Step by step solution

01

Apply change of base formula

We should convert the base 16 logarithm to a base that we can use with our calculator, most commonly base 10 or base 'e'. We can achieve this using the change of base formula. So \( log_{16} 57.2 \) becomes \( \frac{log 57.2}{log 16} \) or \( \frac{ln 57.2}{ln 16} \).
02

Use a calculator to compute the logs

Use a calculator to compute the logs in the numerator and the denominator. For \( log 57.2 \) you will get approximately 1.75812 and for \( log 16 \) you will get approximately 1.20412. If you were to use natural logs, then for \( ln 57.2 \) you get approximately 4.04668 and for \( ln 16 \) you get approximately 2.77259.
03

Perform the Division

Now divide the numerator by the denominator. With common logs, this division yields approximately 1.4591. With natural logs, it also yields approximately 1.4591.
04

Round to four decimal places

Lastly, ensure that the answer fits the criterion of being to four decimal places, by rounding if necessary. The answer in our case is already to four decimal places, so no further rounding is necessary.

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