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: 50

Answer

$\log_b \left(m^2\sqrt{n} \right)$

Work Step by Step

Using the properties of logarithms, the given expression, $ 2\log_b m+\dfrac{1}{2}\log_b n ,$ is equivalent to \begin{array}{l}\require{cancel} \log_b m^2+\log_b n^{1/2} \\\\= \log_b m^2+\log_b \sqrt{n} \\\\= \log_b \left(m^2\sqrt{n} \right) .\end{array}
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