College Algebra (11th Edition)

Published by Pearson

Chapter 4 - Review Exercises - Page 469: 27

Answer

$\log_3 m+\log_3 n-\log_3 5-\log_3 r$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of logarithms to rewrite the given expression, $\log_3 \dfrac{mn}{5r} .$ $\bf{\text{Solution Details:}}$ Using the Quotient Rule of Logarithms, which is given by $\log_b \dfrac{x}{y}=\log_bx-\log_by,$ the expression above is equivalent \begin{array}{l}\require{cancel} \log_3 (mn)-\log_3 (5r) .\end{array} Using the Product Rule of Logarithms, which is given by $\log_b (xy)=\log_bx+\log_by,$ the expression above is equivalent \begin{array}{l}\require{cancel} \log_3 m+\log_3 n-(\log_3 5+\log_3 r) \\\\= \log_3 m+\log_3 n-\log_3 5-\log_3 r .\end{array}

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