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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 282 (page 1045)

In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each logarithm.
$\log_{\sqrt{2}} 17$

Short Answer

Expert verified

The answer is $8.175$

Step by step solution

01

Step 1. Given information

The given logarithmic expression is $\log_{\sqrt{2}} 17$

02

Step 2. Calculate the value

Use the change of base formula that is $\log_{a} M = \frac{\log_{b} M}{\log_{b} a}$

So,

$\log_{\sqrt{2}} 17 = \frac{\log_{10} 17}{\log_{10} \sqrt{2}} = 8.175$

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