Answer
$x\in \{-2, 6\}$
Work Step by Step
$3^{x^2-12}=9^{2x},$
$3^{x^2-12}=3^{4x},$
$x^2-12=4x,$
$x^2-4x-12=0,$
$x^2+2x-6x-12=0,$
$x(x+2)-6(x+2)=0,$
$(x-6)(x+2)=0,$
$x\in \{-2, 6\}$
Intermediate Algebra for College Students (7th Edition)
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13417-894-7
ISBN 13:
978-0-13417-894-3
Chapter 9 - Section 9.5 - Exponential and Logarithmic Equations - Exercise Set - Page 727: 98
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