What is ln(((\sqrt[3]{w^2})z^6)/(x^3y^4)) ?

The solution to ln(((\sqrt[3]{w^2})z^6)/(x^3y^4)) is ln(\sqrt[3]{w^2})+6ln(z)-3ln(x)-4ln(y)

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simplify ln(((\sqrt[3]{w^2})z^6)/(x^3y^4))

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 (z^{6}) = 6 ln (z)

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

Apply log rule:

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

ln (y^{4}) = 4 ln (y)

- (3 ln (x) + 4 ln (y)) : - 3 ln (x) - 4 ln (y)

ln (\frac{1}{x !})

lo g_{b} (\frac{x ^{2} \cdot y}{z ^{6}})

\frac{1}{2} lo g_{4} (25) + lo g_{4} (2)

- \frac{2}{3} lo g_{b} (x + 1) - \frac{1}{4} lo g_{b} (x + 2)

ln (\frac{e ^{8 x} + 1}{e ^{- 3 x} + 1})

What is ln(((\sqrt[3]{w^2})z^6)/(x^3y^4)) ?
The solution to ln(((\sqrt[3]{w^2})z^6)/(x^3y^4)) is ln(\sqrt[3]{w^2})+6ln(z)-3ln(x)-4ln(y)