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: 46


$\frac{1}{2}log_{b}3-\frac{1}{2}log_{b} y$

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, $log_{b}\sqrt(\frac{3}{y})= log_{b}\frac{\sqrt 3}{\sqrt y}= log_{b}\sqrt 3-log_{b}\sqrt y= log_{b}3^{\frac{1}{2}}-log_{b} y^{\frac{1}{2}}$. 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_{b}3^{\frac{1}{2}}-log_{b} y^{\frac{1}{2}}=\frac{1}{2}log_{b}3-\frac{1}{2}log_{b} y$.
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