Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.3 - Properties of Logarithms - Exercise Set - Page 475: 28

Answer

$3\log_{b}x+\log_{b}y-2\log_{b}z $

Work Step by Step

$\displaystyle \log_{b}(\frac{x^{3}y}{z^{2}})=$ ...apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$ $=\log_{b}(x^{3}y)-\log_{b}z^{2}$ $\qquad $...apply the Product Rule: $\qquad \log_{b}(MN)=\log_{b}\mathrm{M}+\log_{b}\mathrm{N}$ $\displaystyle =\log_{b}x^{3}+\log_{b}y-\log_{b}z^{2}$ $\quad $...apply the Power Rule: $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$ = $3\log_{b}x+\log_{b}y-2\log_{b}z $
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