Intermediate Algebra (6th Edition)

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

Chapter 9 - Section 9.6 - Properties of Logarithms - Exercise Set: 51

Answer

$2log_{6}x-log_{6}(x+3)$

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, $log_{6}\frac{x^{2}}{(x+3)}= log_{6}x^{2}-log_{6}(x+3)$. 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_{6}x^{2}-log_{6}(x+3)= 2log_{6}x-log_{6}(x+3)$.
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