Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Sections 9.1-9.6 - Integrated Review - Functions and Properties of Logarithms: 32

Answer

$log_{5}\frac{x^{3}}{y^{5}}$

Work Step by Step

The power property of logarithms tells us that $log_{b}x^{r}=r log_{b}x$ (where x and b are positive real numbers, $b\ne1$, and r is a real number). Therefore, $3log_{5}x-5log_{5}y=log_{5}x^{3}-log_{5}y^{5}$. 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_{5}x^{3}-log_{5}y^{5}=log_{5}\frac{x^{3}}{y^{5}}$.
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