Answer
$16$.
Work Step by Step
Based on the given conditions, we have $f(\frac{1}{2})=log_a(\frac{1}{2})=-4 \Longrightarrow a^{-4}=\frac{1}{2} \Longrightarrow a=16$.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 4 - Exponential and Logarithmic Functions - Section 4.4 Logarithmic Functions - 4.4 Assess Your Understanding - Page 321: 58
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