Answer
$log_{4}(\frac{1}{8})=-\frac{3}{2}$
Work Step by Step
Use the definition $b^y=x$ is equivalent to $y=log_b(x)$, we have $(4)^{-3/2}=\frac{1}{8}$ is equivalent to $-\frac{3}{2}=log_{4}(\frac{1}{8})$ or $log_{4}(\frac{1}{8})=-\frac{3}{2}$
Precalculus (6th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
013421742X
ISBN 13:
978-0-13421-742-0
Chapter 4 - Inverse, Exponential, and Logarithmic Functions - Summary Exercises on Inverse, Exponential, and Logarithmic Functions - Exercises - Page 449: 24
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