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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. 10.72 (page 1042)

Use the Properties of Logarithms to condense the logarithm $2 \log x + 2 \log (x + 1) .$ Simplify, if possible.

Short Answer

Expert verified

The condensed form of the logarithm is $\log x^{2} {(x + 1)}^{2} .$

Step by step solution

01

Step 1. Given Infomation

The given logarithm is $2 \log x + 2 \log (x + 1) .$

We have to use the Properties of Logarithms to condense the logarithm.

02

Step 2. Use the Power Property of the logarithm

The power property of the logarithm is $\log_{a} M^{p} = p \log_{a} M$

So,

role="math" localid="1644996806106" $2 \log x + 2 \log (x + 1) = \log x^{2} + \log {(x + 1)}^{2}$

03

Step 3. Use the Product Property of logarithm

The Product Property of logarithm is $\log_{a} M 路 N = \log_{a} M + \log_{a} N .$

So,

$= \log x^{2} + \log {(x + 1)}^{2} = \log x^{2} {(x + 1)}^{2}$

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