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Chapter 5: Q 75. (page 309)

Use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places.
$\log_{\sqrt{2}} 7$

Short Answer

Expert verified

$5.615$

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\log_{\sqrt{2}} 7$

02

Step 2. Calculation.

Apply the base change formula and simplify.

$\begin{array}{l} \log_{\sqrt{2}} 7 = \frac{\log 7}{\log \sqrt{2}} \\ = \frac{\log 7}{\frac{1}{2} \log 2} \\ = 2 (\frac{\log 7}{\log 2}) \\ = 2 (2.80735) \\ \approx 5.615 \end{array}$

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Most popular questions from this chapter

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red

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See all solutions

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