Answer
$x=-2$or $x=6$.
Work Step by Step
We know that $a^b=a^c\longrightarrow b=c$ if $a\ne1,a\ne-1$ (which applies here).
Hence here $25^{2x}=5^{x^2-12}=2^2\\(5^2)^{2x}=5^{x^2-12}\\4x=x^2-12\\x^2-4x-12=0\\(x+2)(x-6)=0$
Thus $x=-2$or $x=6$.
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter 6 - Review Exercises - Page 500: 38
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