Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - Mid-Chapter Review - Mixed Review - Page 812: 17


$ \displaystyle \log x-\frac{1}{2}\log y-\frac{3}{2}\log z$

Work Step by Step

.... first, write the square root as a power with exponent 1/2 $...=\displaystyle \log(\frac{x^{2}}{yz^{3}})^{1/2}\quad$... Apply the property $\log_{a}M^{p}=p\cdot\log_{a}M$ $=\displaystyle \frac{1}{2}\log\frac{x^{2}}{yz^{3}}\quad$... Apply the property $\displaystyle \log_{a}\frac{M}{N}=\log_{a}M-\log_{a}N$ $=\displaystyle \frac{1}{2}[\log x^{2}-\log(yz^{3})]\quad$... Apply the property $\log_{a}(MN)=\log_{a}M+\log_{a}N$ $=\displaystyle \frac{1}{2}[\log x^{2}-(\log y+\log z^{3})]$ $=\displaystyle \frac{1}{2}[\log x^{2}-\log y-\log z^{3}]\quad$... Apply the property $\log_{a}M^{p}=p\cdot\log_{a}M$ $=\displaystyle \frac{1}{2}[2\log x-\log y-3\log z]$ $=\displaystyle \log x-\frac{1}{2}\log y-\frac{3}{2}\log z$
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