## Intermediate Algebra (6th Edition)

Published by Pearson

# Chapter 9 - Section 9.6 - Properties of Logarithms - Exercise Set: 40

#### Answer

$log_{7}5+log_{7}x-log_{7}4$

#### Work Step by Step

The quotient property of logarithms tells us that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$). Therefore, $log_{7}\frac{5x}{4}=log_{7}5x-log_{7}4$. The product property of logarithms tells us that $log_{b}xy=log_{b}x+log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$). Therefore, $log_{7}5x-log_{7}4= log_{7}5+log_{7}x-log_{7}4$.

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