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

The solution to 9ln(x)-1/8 ln(y) is ln((x^9y^{7/8})/y)

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

simplify

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

ln (\frac{x ^{9} y ^{\frac{7}{8}}}{y})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{9}}{y ^{\frac{1}{8}}} : \frac{x ^{9} y ^{\frac{7}{8}}}{y}

= ln (\frac{x ^{9} y ^{\frac{7}{8}}}{y})

lo g_{3} (4 x^{2} y^{5})

ln (\frac{s ^{2} + 9}{s ^{2} + 1})

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

ln (\frac{5}{12})

lo g_{a} (ab) - lo g_{a} (a^{3} b)

What is 9ln(x)-1/8 ln(y) ?
The solution to 9ln(x)-1/8 ln(y) is ln((x^9y^{7/8})/y)