Answer
$x=-3$
Work Step by Step
$4(3^{-2x-4})=36$
$\implies 3^{-2x-4}=\frac{36}{4}=9$
$\implies 3^{-2x-4}=3^{2}$
For the above equality to hold, the exponents must be equal.
$\implies -2x-4=2$
$\implies -2x=2+4$
$\implies x=\frac{6}{-2}=-3$
Big Ideas Math - Algebra 1, A Common Core Curriculum
by Larson, Ron; Boswell, Laurie
Published by
Big Ideas Learning LLC
ISBN 10:
978-1-60840-838-2
ISBN 13:
978-1-60840-838-2
Chapter 6 - Exponential Functions and Sequences - 6.5 - Solving Exponential Equations - Exercises - Page 330: 39
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