Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.3 One-to-One Functions; Inverse Functions - 5.3 Assess Your Understanding: 85

Answer

$=\dfrac {1}{4}$

Work Step by Step

$a^{m\times n}=\left( a^{m}\right) ^{n}\Rightarrow 3^{2x}=\left( 3^{-x}\right) ^{-2}$ Since $3^{-x}=2$, then $(3^{-x})^{-2} = 2^{-2}$ Using the rule $a^{-m} = \dfrac{1}{a^m}$ gives: $(3^{-x})^{-2} = \dfrac{1}{2^2} =\dfrac{1}{4}$
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