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: 36

Answer

$log_{7}9+2log_{7}x-log_{7}y $

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, $log_{7}\frac{9x^{2}}{y}=log_{7}9x^{2}-log_{7}y$. 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}9x^{2}-log_{7}y= log_{7}9+log_{7}x^{2}-log_{7}y $. 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, $ log_{7}9+log_{7}x^{2}-log_{7}y= log_{7}9+2log_{7}x-log_{7}y $.
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