Answer
$2^x=10$.
Work Step by Step
We know that $\frac{1}{1000}=\frac{1}{10^3}=10^{-3}$ and that $2^{-3x}=(2^x)^{-3}.$
Hence $2^{-3x}=\frac{1}{1000}\\(2^x)^{-3}=10^{-3}$.
We know that $a^b=c^b\longrightarrow a=c$ if $b\ne1$.
Thus $2^x=10$.
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: 88
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