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

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

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

expand

- \frac{1}{3} ln (x^{5} - 2 x^{4})

Solution steps

Rewrite as

= ln ((\frac{1}{x ^{5} - 2 x ^{4}})^{\frac{1}{3}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{3} ln (\frac{1}{x ^{5} - 2 x ^{4}})

Simplify

ln (\frac{1}{x ^{5} - 2 x ^{4}}) : - ln (x^{5} - 2 x^{4})

= \frac{1}{3} (- ln (x^{5} - 2 x^{4}))

Remove parentheses:

(- a) = - a

= - \frac{1}{3} ln (x^{5} - 2 x^{4})

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