What is 9ln(x)-1/2 ln(y) ?

The solution to 9ln(x)-1/2 ln(y) is ln((x^9sqrt(y))/y)

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simplify 9ln(x)-1/2 ln(y)

simplify

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

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

Solution steps

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

Apply log rule:

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

\frac{1}{2} ln (y) = ln (y^{\frac{1}{2}})

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{9}}{y ^{\frac{1}{2}}} : \frac{x ^{9} y}{y}

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

ln (e^{iπ}) - ln (3 e^{iπ} + 4)

8 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)

lo g_{10} (x^{2} y^{3} z^{4})

lo g_{10} (x) + 2 lo g_{10} (y) - 3 lo g_{10} (a)

ln (2 x) - ln (x)

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