Answer
$log\frac{x+2}{x+1}$
Work Step by Step
$log(x^2+3x+2)-2log(x+1)=log[(x+2)(x+1)]-log(x+1)^2=log\frac{(x+2)(x+1)}{(x+1)^2}=log\frac{x+2}{x+1}$
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 5 - Exponential and Logarithmic Functions - 5.5 Properties of Logarithms - 5.5 Assess Your Understanding - Page 305: 62
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