Answer
$x=-2.$
Work Step by Step
$9^{x+1}=(3^2)^{x+1}=3^{2(x+1)}=3^{2x+2}$, hence the equation becomes: $3^{x}=3^{2x+2}$.
We know that if $a\ne1,-1$, then $a^k=a^l\longrightarrow k=l$.
Hence: $2x+2=x\\(2x+2)-x=x-x\\x+2=0\\(x+2)-2=0-2\\x=-2.$
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 11 - Systems of Equations and Inequalities - Chapter Review - Cumulative Review - Page 797: 4
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