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: 35

Answer

$ log_{3}\frac{(y^{4}+11y)}{(y+2)}$

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, $log_{3}y-log_{3}(y+2)+log_{3}(y^{3}+11)= log_{3}\frac{y}{(y+2)}+log_{3}(y^{3}+11)$. 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_{3}\frac{y}{(y+2)}+log_{3}(y^{3}+11)= log_{3}(\frac{y}{(y+2)}\times (y^{3}+11))=log_{3}\frac{y(y^{3}+11)}{(y+2)}= log_{3}\frac{(y^{4}+11y)}{(y+2)}$.
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