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: 56

Answer

$\log_a \dfrac{2x^4}{y^3}$

Work Step by Step

Using the properties of logarithms, the given expression, $ \log_a 2x+3(\log_ax-\log_ay) ,$ simplifies to \begin{array}{l}\require{cancel} \log_a 2x+3\log_ax-3\log_ay \\\\= \log_a 2x+\log_ax^3-\log_ay^3 \\\\= \log_a \dfrac{2x\cdot x^3}{y^3} \\\\= \log_a \dfrac{2x^4}{y^3} .\end{array}
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