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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