What is 8ln(x)-1/6 ln(y) ?

The solution to 8ln(x)-1/6 ln(y) is ln((x^8y^{5/6})/y)

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simplify 8ln(x)-1/6 ln(y)

simplify

8 ln (x) - \frac{1}{6} ln (y)

ln (\frac{x ^{8} y ^{\frac{5}{6}}}{y})

Solution steps

8 ln (x) - \frac{1}{6} 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}{6} ln (y)

Apply log rule:

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

\frac{1}{6} ln (y) = ln (y^{\frac{1}{6}})

= ln (x^{8}) - ln (y^{\frac{1}{6}})

Apply log rule:

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

ln (x^{8}) - ln (y^{\frac{1}{6}}) = ln (\frac{x ^{8}}{y ^{\frac{1}{6}}})

= ln (\frac{x ^{8}}{y ^{\frac{1}{6}}})

Simplify

\frac{x ^{8}}{y ^{\frac{1}{6}}} : \frac{x ^{8} y ^{\frac{5}{6}}}{y}

= ln (\frac{x ^{8} y ^{\frac{5}{6}}}{y})

lo g_{4} (\frac{x - 4}{y ^{2} ( 5 z )})

lo g_{7} (\frac{49 b ^{7} y ^{2} - 9}{y ( x + 9 ) ^{2}})

lo g_{7} (x) - lo g_{7} (x^{11})

ln (x^{9}) - ln (x)

ln (πi)

What is 8ln(x)-1/6 ln(y) ?
The solution to 8ln(x)-1/6 ln(y) is ln((x^8y^{5/6})/y)