Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.3 - Logarithmic Functions - Exercise Set: 27

Answer

$x=-3$

Work Step by Step

First, we let $\log_{2}{\frac{1}{8}} = x$ RECALL: $\log_b{y} =x \longrightarrow b^x=y$ Use the rule above, where $y=\frac{1}{8}$ and $b=2$, to obtain: $2^x=\frac{1}{8}$ Write $\frac{1}{8}$ as $ 2^{-3}$ to obtain: $2^x=2^{-3}$ Use the rule "If $a^x=a^y$, then $x=y$" to obtain: $x=-3$
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