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 - Chapter Review - Review Exercises - Page 345: 22



Work Step by Step

Recall: (1) $\sqrt[m]{a}=a^{\frac{1}{m}}$ (2) $\log_a {x^n}=n\cdot \log_a {x}$. (3) $\log_a{xy}=\log_a{x} +\log_a{y}$ (4) $\log_a{\frac{x}{y}}=\log_a{x} -\log_a{y}$ ($\log_a{M}=\log_a{N} \longrightarrow M=N$.) Using Rule(2): $\log_2{(a^2\sqrt b)^4}=4\log_2{a^2\sqrt b}.$ Using Rule(3): $4\log_2{a^2\sqrt b}=4\log_2{a^2}+\log_2{\sqrt b}$ Using Rule(2): $4\log_2{a^2}+\log_2{\sqrt b}=4[2\log_2{a}+\frac{1}{2}\log_2{b}]=8\log_2{a}+2\log_2{b}$
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