What is ln((5x^2\sqrt[3]{1-x})/(4(x+1)^2)) ?

The solution to ln((5x^2\sqrt[3]{1-x})/(4(x+1)^2)) is ln(5)+2ln(x)+ln(\sqrt[3]{1-x})-2ln(2)-2ln(x+1)

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simplify ln((5x^2\sqrt[3]{1-x})/(4(x+1)^2))

simplify

Solution steps

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{2}) = 2 ln (x)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x + 1)^{2}) = 2 ln (x + 1)

ln (4) = 2 ln (2)

- (2 ln (2) + 2 ln (x + 1)) : - 2 ln (2) - 2 ln (x + 1)

lo g_{8} (\frac{8}{y})

lo g_{4} (5 r)

lo g_{10} (\frac{a ^{2}}{b ^{- 3} c ^{4}})

ln (2 e^{- x})

\frac{1}{2} ln (5)

What is ln((5x^2\sqrt[3]{1-x})/(4(x+1)^2)) ?
The solution to ln((5x^2\sqrt[3]{1-x})/(4(x+1)^2)) is ln(5)+2ln(x)+ln(\sqrt[3]{1-x})-2ln(2)-2ln(x+1)