Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set: 41

Answer

$\log_b x+2\log_b y-\log_b w-3\log_b z$

Work Step by Step

Using the properties of logarithms, the given expression, $ \log_b \dfrac{xy^2}{wz^3} ,$ is equivalent to \begin{array}{l}\require{cancel} \log_b (xy^2)-\log_b (wz^3) \\\\= \log_b x+\log_b y^2-\left( \log_b w+\log_b z^3 \right) \\\\= \log_b x+\log_b y^2-\log_b w-\log_b z^3 \\\\= \log_b x+2\log_b y-\log_b w-3\log_b z .\end{array}
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