What is ln(((3y^3-3)/(x^3))^{-2/9})-ln(x) ?

The solution to ln(((3y^3-3)/(x^3))^{-2/9})-ln(x) is -ln(x^{1/3}(3y^3-3)^{2/9})

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simplify ln(((3y^3-3)/(x^3))^{-2/9})-ln(x)

simplify

ln ((\frac{3 y ^{3} - 3}{x ^{3}})^{- \frac{2}{9}}) - ln (x)

- ln (x^{\frac{1}{3}} (3 y^{3} - 3)^{\frac{2}{9}})

Solution steps

ln ((\frac{3 y ^{3} - 3}{x ^{3}})^{- \frac{2}{9}}) - ln (x)

Apply log rule:

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

ln ((\frac{3 y ^{3} - 3}{x ^{3}})^{- \frac{2}{9}}) - ln (x) = ln \frac{( \frac{3 y ^{3} - 3}{x ^{3}} ) ^{- \frac{2}{9}}}{x}

= ln \frac{( \frac{3 y ^{3} - 3}{x ^{3}} ) ^{- \frac{2}{9}}}{x}

Simplify

\frac{( \frac{3 y ^{3} - 3}{x ^{3}} ) ^{- \frac{2}{9}}}{x} : \frac{1}{x ^{\frac{1}{3}} ( 3 y ^{3} - 3 ) ^{\frac{2}{9}}}

= ln (\frac{1}{x ^{\frac{1}{3}} ( 3 y ^{3} - 3 ) ^{\frac{2}{9}}})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (x^{\frac{1}{3}} (3 y^{3} - 3)^{\frac{2}{9}})

lo g_{10} (\frac{4}{5 x})

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

ln (\frac{p}{( 1 - p )})

2 ln (x) + ln (y) - 4 x - y

\frac{4}{3} ln ∣ x - 1 ∣ - \frac{1}{3} ln ∣ x - 4 ∣

What is ln(((3y^3-3)/(x^3))^{-2/9})-ln(x) ?
The solution to ln(((3y^3-3)/(x^3))^{-2/9})-ln(x) is -ln(x^{1/3}(3y^3-3)^{2/9})