Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding: 56

$\ln 5-\ln 4+2\ln x+\dfrac {1}{3}\ln \left( 1-x\right) -2\ln \left( x+1\right)$

Work Step by Step

We use the rules of logarithms to obtain: $\ln \dfrac {5x^{2}\sqrt [3] {1-x}}{4\left( x+1\right) ^{2}}=\ln 5+\ln x^{2}+\ln \left( 1-x\right) ^{\dfrac {1}{3}}-\ln 4-\ln \left( x+1\right) ^{2}=\ln 5-\ln 4+2\ln x+\dfrac {1}{3}\ln \left( 1-x\right) -2\ln \left( x+1\right)$

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