Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Section 4.4 - Laws of Logarithms - 4.4 exercises - Page 359: 46


$\log x$ - $\frac{1}{3}$$\log (1-x)$

Work Step by Step

$Expand$ $the$ $expression$: $\log (\frac{x}{\sqrt[3]{1-x}})$ Apply the Second Law of Logarithms $\log (\frac{x}{\sqrt[3]{1-x}})$ = $\log x$ - $\log \sqrt[3]{1-x}$ Rewrite the cube root $\log x$ - $\log (1-x)^\frac{1}{3}$ Apply the Third Law of Logarithms for $\log (1-x)^\frac{1}{3}$ $\log (1-x)^\frac{1}{3}$ = $\frac{1}{3}$$\log (1-x)$ $\log x$ - $\frac{1}{3}$$\log (1-x)$
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