Answer
$x=\frac{1}{2}$
Work Step by Step
We need to solve:
$3^{4x}-3^{2x}-6=0$
We factor:
$(3^{2x}-3)(3^{2x}+2)=0$
$(3^{2x}-3)=0$ or $(3^{2x}+2)=0$
$3^{2x}=3$ or $3^{2x}=-2$
$2x=\log_3 3=1$ or $2x=\log_3 -2$=no solution
$2x=1$
$x=\frac{1}{2}$
College Algebra 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305115546
ISBN 13:
978-1-30511-554-5
Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 42
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