Answer
$\frac{5}{2}$
Work Step by Step
$log_3(x-1)+log_3(2x+1)=2$,
$log_3[(x-1)(2x+1)]=2$,
$2x^2+x-2x-1=3^2$,
$2x^2-x-10=0$,
$(2x-5)(x+2)=0$,
thus $x=-2, \frac{5}{2}$,
check only $x=\frac{5}{2}$ fits.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 10 - Systems of Equations and Inequalities - Cumulative Review - Page 817: 5
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