Answer
$x=0$
Work Step by Step
Apply $\log$ to both sides and then isolate $x$ as follows:
$\log (1.2^{x})=\log(0.5)^{-x} \\ x\log(1.2)=-x\log(0.5) \\ x\log(1.2)+x\log(0.5)=0 \\ x [\log(1.2)+\log(0.5)]=0 \\ x=0$
Thus, our answer is: $x=0$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 53
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