Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

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: 29



Work Step by Step

Since $y=\log_a x \text{ is equivalent to } x= a^y$ Thus, if $y = \log_{1/2} 16$, then $\left(\dfrac{1}{2}\right)^y=16$. Note that: $16=2^4=\left(\dfrac{1}{2}\right)^{-4}$ Therefore, $\left(\dfrac{1}{2}\right)^y=\left(\dfrac{1}{2}\right)^{-4}$ Use the rule $a^m=a^n \implies m=n$ to obtain: $y=-4$ Hence, $ \log_{1/2} 16 = \boxed{-4}$
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