What is expand ln((x(4y-1)^{1/3})^{2/5}) ?

The solution to expand ln((x(4y-1)^{1/3})^{2/5}) is 2/5 ln(x)+2/15 ln(4y-1)

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expand ln((x(4y-1)^{1/3})^{2/5})

expand

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

\frac{2}{5} ln (x) + \frac{2}{15} ln (4 y - 1)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln ((4 y - 1)^{\frac{1}{3}}) = \frac{1}{3} ln (4 y - 1)

= \frac{2}{5} ln (x) + \frac{2}{5} \cdot \frac{1}{3} ln (4 y - 1)

\frac{2}{5} \cdot \frac{1}{3} ln (4 y - 1) = \frac{2}{15} ln (4 y - 1)

= \frac{2}{5} ln (x) + \frac{2}{15} ln (4 y - 1)

ln (4 e^{2 x})

lo g_{5} (\frac{x}{25})

lo g_{10} (x^{5}) y^{3}

lo g_{3} (\frac{p ^{2}}{u w})

ln (\frac{a ^{- 2}}{b ^{- 4} c ^{5}})

What is expand ln((x(4y-1)^{1/3})^{2/5}) ?
The solution to expand ln((x(4y-1)^{1/3})^{2/5}) is 2/5 ln(x)+2/15 ln(4y-1)