Intermediate Algebra (6th Edition)

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

Chapter 9 - Review: 71

Answer

$log_{5}\frac{x^{3}}{(x+1)^{2}}$

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, $2log_{5}x-2log_{5}(x+1)+log_{5}x=log_{5}x^{2}-log_{5}(x+1)^{2}+log_{5}x$. 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, $log_{5}x^{2}-log_{5}(x+1)^{2}+log_{5}x=log_{5}\frac{x^{2}}{(x+1)^{2}}+log_{5}x$. 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, $log_{5}\frac{x^{2}}{(x+1)^{2}}+log_{5}x=log_{5}\frac{(x^{2}\times x)}{(x+1)^{2}}=log_{5}\frac{x^{3}}{(x+1)^{2}}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.