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 4.5 Properties of Logarithms - 4.5 Assess Your Understanding - Page 331: 46


$\log_2 a - 2\log_2 b$

Work Step by Step

Recall: $\log_a\left(\dfrac{M}{N}\right) = \log_a M-\log_a N$ Using the rule above gives; $\log_2 \left(\dfrac{a}{b^2} \right) = \log_2 a-\log_2 b^2$ Note that $\log_a M^r = r \log_a M$ Therefore, the expression above simplifies to: $\log_2 \left(\dfrac{a}{b^2} \right) = \boxed{\log_2 a - 2\log_2 b}$
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