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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. 10.71 (page 1042)

Use the Properties of Logarithms to condense the logarithm $3 \log_{2} x + 2 \log_{2} (x - 1)$ . Simplify, if possible.

Short Answer

Expert verified

The condensed form of the logarithm is $3 \log_{2} x + 2 \log_{2} (x - 1) = \log_{2} x^{3} {(x - 1)}^{2}$

Step by step solution

01

Step 1. given data

Given logarithm expressions is $3 \log_{2} x + 2 \log_{2} (x - 1)$

02

Step 2. Apply power Property of the logarithm

Use power Property of the logarithm $p \log_{a} (m) = \log_{a} (m^{p})$

role="math" localid="1644962279660" $3 \log_{2} x + 2 \log_{2} (x - 1) = \log_{2} x^{3} + \log_{2} {(x - 1)}^{2}$

03

Step 3. apply product Properties of Logarithms

Use product Properties of Logarithms $\log_{a} m + \log_{a} n = \log_{a} (m 路 n)$

$3 \log_{2} x + 2 \log_{2} (x - 1) = \log_{2} x^{3} + \log_{2} {(x - 1)}^{2} 3 \log_{2} x + 2 \log_{2} (x - 1) = \log_{2} x^{3} {(x - 1)}^{2}$

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Most popular questions from this chapter

In the following exercises, solve each equation.

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