Answer
$x=-4$
Work Step by Step
Since $16=2^4$, then $2^{-x}=2^4$
The base is same on the 2 sides of the equation (and it is not 1), hence they will be equal if the exponents are equal.
Thus,
$-x=4\\
-x(1)=4(-1)\\
x=-4$
Precalculus (10th Edition)
by Sullivan, Michael
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 - Page 282: 65
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