What is 3ln(x)-1/4 ln(y) ?

The solution to 3ln(x)-1/4 ln(y) is ln((x^3y^{3/4})/y)

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simplify 3ln(x)-1/4 ln(y)

simplify

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

ln (\frac{x ^{3} y ^{\frac{3}{4}}}{y})

Solution steps

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

Apply log rule:

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

3 ln (x) = ln (x^{3})

= ln (x^{3}) - \frac{1}{4} ln (y)

Apply log rule:

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

\frac{1}{4} ln (y) = ln (y^{\frac{1}{4}})

= ln (x^{3}) - ln (y^{\frac{1}{4}})

Apply log rule:

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

ln (x^{3}) - ln (y^{\frac{1}{4}}) = ln (\frac{x ^{3}}{y ^{\frac{1}{4}}})

= ln (\frac{x ^{3}}{y ^{\frac{1}{4}}})

Simplify

\frac{x ^{3}}{y ^{\frac{1}{4}}} : \frac{x ^{3} y ^{\frac{3}{4}}}{y}

= ln (\frac{x ^{3} y ^{\frac{3}{4}}}{y})

lo g_{4} (5) + lo g_{4} (x) + lo g_{4} (y)

ln (\frac{2 x ^{5}}{y ^{7}})

\frac{1}{2} ln (\frac{x + 1}{x - 1}) + e^{s i n^{2} (x)} + ln (3)

2 lo g_{10} (y) + lo g_{10} (x)

\frac{1}{2} lo g_{a} (x) + 5 lo g_{a} (y) - 3 lo g_{a} (x)

What is 3ln(x)-1/4 ln(y) ?
The solution to 3ln(x)-1/4 ln(y) is ln((x^3y^{3/4})/y)