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 - 5.4 Logarithmic Functions - 5.4 Assess Your Understanding - Page 295: 60



Work Step by Step

We know that if the graph of $f(x)=\log_a{x}$ contains the point $\left(\frac{1}{2},-4\right)$, then $-4=\log_a{\frac{1}{2}}$. We know that if $y=\log_a{b}$, then $a^y=b$. Hence here: $a^{-4}=\frac{1}{2}\\a^4=2\\a=\pm\sqrt[4]2.$ But the base of a logarithm can only be positive, hence $a=\sqrt[4]2.$
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