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: 42

Answer

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

Work Step by Step

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