College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.4 - Laws of Logarithms - 4.4 Exercises: 48

Answer

$\frac{1}{2}\log x+\frac{1}{4}\log y+\frac{1}{8}\log z$

Work Step by Step

$\log\sqrt{x\sqrt{y\sqrt{z}}}=\log(x\sqrt{y\sqrt{z}})^{1/2}=\frac{1}{2}\log(x\sqrt{y\sqrt{z}})=\frac{1}{2}(\log x+\log\sqrt{y\sqrt{z}})=\frac{1}{2}[\log x+\frac{1}{2}\log(y\sqrt{z})]=\frac{1}{2}[\log x+\frac{1}{2}(\log y+\frac{1}{2}\log z)]=\frac{1}{2}\log x+\frac{1}{4}\log y+\frac{1}{8}\log z$
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