Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Review - Test - Page 391: 5

Answer

a) $ \log x + 3\log y - 2\log z $ b) $\frac{1}{2} \ln x - \frac{1}{2} \ln y$ c) $ \frac{1}{3} \log (x+2) - \frac{4}{3}\log x-\frac{1}{3}\log(x^{2}+4)$

Work Step by Step

Use the basic Laws of Logarithms to expand the espressions: a) $\log(\frac{xy^{3}}{z^{2}})= \log x + 3\log y - 2\log z $ b) $\ln\sqrt \frac{x}{y}=\frac{1}{2} \ln x - \frac{1}{2} \ln y$ c) $ \log\sqrt[3] \frac{x+2}{x^{4}(x^{2}+4)}=\log\sqrt[3] {x+2} - \log \sqrt[3] {x^{4}(x^{2}+4)}= \frac{1}{3} \log (x+2) - \frac{1}{3}\log (x^{4}(x^{2}+4))=\frac{1}{3} \log (x+2) - [\frac{1}{3}\log x^{4}+\frac{1}{3}\log(x^{2}+4)]=\frac{1}{3} \log (x+2) - \frac{4}{3}\log x-\frac{1}{3}\log(x^{2}+4)$
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