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 - Page 282: 88



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 $2^x=10$.
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