What is 8ln(x)-1/9 ln(y) ?

The solution to 8ln(x)-1/9 ln(y) is ln((x^8y^{8/9})/y)

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simplify 8ln(x)-1/9 ln(y)

simplify

8 ln (x) - \frac{1}{9} ln (y)

ln (\frac{x ^{8} y ^{\frac{8}{9}}}{y})

Solution steps

8 ln (x) - \frac{1}{9} ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

8 ln (x) = ln (x^{8})

= ln (x^{8}) - \frac{1}{9} ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{9} ln (y) = ln (y^{\frac{1}{9}})

= ln (x^{8}) - ln (y^{\frac{1}{9}})

Apply log rule:

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

ln (x^{8}) - ln (y^{\frac{1}{9}}) = ln (\frac{x ^{8}}{y ^{\frac{1}{9}}})

= ln (\frac{x ^{8}}{y ^{\frac{1}{9}}})

Simplify

\frac{x ^{8}}{y ^{\frac{1}{9}}} : \frac{x ^{8} y ^{\frac{8}{9}}}{y}

= ln (\frac{x ^{8} y ^{\frac{8}{9}}}{y})

lo g_{10} (\frac{x}{z ^{6}})

lo g_{10} (28) - lo g_{10} (7)

lo g_{3} (9^{2} \cdot 2^{4})

ln (x^{7} 2 - x)

lo g_{b} (7) + 2 lo g_{b} (2)

What is 8ln(x)-1/9 ln(y) ?
The solution to 8ln(x)-1/9 ln(y) is ln((x^8y^{8/9})/y)