## College Algebra (11th Edition)

Published by Pearson

# Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 424: 77

#### Answer

$\log_a\dfrac{m}{nt}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Laws of Logarithms to write the given expression, $\log_am-\log_an-\log_at ,$ as a single logarithm. $\bf{\text{Solution Details:}}$ Grouping the last two terms, the expression above is equivalent to \begin{array}{l}\require{cancel} \log_am-(\log_an+\log_at) .\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_am-(\log_a(nt)) .\end{array} 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_a\dfrac{m}{nt} .\end{array}

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