Intermediate Algebra (6th Edition)

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

Chapter 9 - Review: 76

Answer

$log_{7}y+3log_{7}z-log_{7}x$

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, $log_{7}\frac{yz^{3}}{x}=log_{7}(yz^{3})-log_{7}x$. 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, $log_{7}(yz^{3})-log_{7}x=log_{7}y+log_{7}z^{3}-log_{7}x$. 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, $log_{7}y+log_{7}z^{3}-log_{7}x=log_{7}y+3log_{7}z-log_{7}x$
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