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

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

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

simplify

Solution steps

Apply log rule:

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

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

Apply radical rule:

assuming

a \geq 0, b \geq 0

lo g_{10} (z^{7} y)

ln (\frac{x - 1}{x - 2})

- \frac{8}{14} lo g_{2} (\frac{8}{14}) - \frac{6}{14} lo g_{2} (\frac{6}{14})

lo g_{10} (\frac{5}{36}) - lo g_{10} (\frac{5}{9})

- \frac{1}{44.6} ln (\frac{1}{2})

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