Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.2 Exponential Functions - 4.2 Exercises: 94

Answer

$-3$

Work Step by Step

$\left( \sqrt [3] {5}\right) ^{-x}=\left( \dfrac {1}{5}\right) ^{x+2}\Rightarrow \left( 5^{\dfrac {1}{3}}\right) ^{-x}=\left( 5^{-1}\right) ^{x+2}\Rightarrow 5^{-\dfrac {x}{3}}=5^{-\left( x+2\right) }\Rightarrow -\dfrac {x}{3}=-\left( x+2\right) \Rightarrow \dfrac {2x}{3}=-2\Rightarrow x=-3$
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