What is 3ln(x)-5ln(y)-1/4 ln(x) ?

The solution to 3ln(x)-5ln(y)-1/4 ln(x) is ln((x^{11/4})/(y^5))

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simplify 3ln(x)-5ln(y)-1/4 ln(x)

simplify

3 ln (x) - 5 ln (y) - \frac{1}{4} ln (x)

ln (\frac{x ^{\frac{11}{4}}}{y ^{5}})

Solution steps

3 ln (x) - 5 ln (y) - \frac{1}{4} ln (x)

Apply log rule:

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

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

= ln (x^{3}) - 5 ln (y) - \frac{1}{4} ln (x)

Apply log rule:

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

5 ln (y) = ln (y^{5})

= ln (x^{3}) - ln (y^{5}) - \frac{1}{4} ln (x)

Apply log rule:

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

ln (x^{3}) - ln (y^{5}) = ln (\frac{x ^{3}}{y ^{5}})

= ln (\frac{x ^{3}}{y ^{5}}) - \frac{1}{4} ln (x)

Apply log rule:

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

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

= ln (\frac{x ^{3}}{y ^{5}}) - ln (x^{\frac{1}{4}})

Apply log rule:

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

ln (\frac{x ^{3}}{y ^{5}}) - ln (x^{\frac{1}{4}}) = ln (\frac{\frac{x ^{3}}{y ^{5}}}{x ^{\frac{1}{4}}})

= ln (\frac{\frac{x ^{3}}{y ^{5}}}{x ^{\frac{1}{4}}})

Simplify

\frac{\frac{x ^{3}}{y ^{5}}}{x ^{\frac{1}{4}}} : \frac{x ^{\frac{11}{4}}}{y ^{5}}

= ln (\frac{x ^{\frac{11}{4}}}{y ^{5}})

lo g_{3} (\frac{x + 33 x}{( x - 1 ) ( x - 5 )})

lo g_{2} (\frac{1}{2} x^{2} y)

ln (\frac{e ^{3} 2}{e ^{\frac{1}{3}}}) - e^{2 l n (2)}

- ln (a) - ln (b)

ln (11 x)

What is 3ln(x)-5ln(y)-1/4 ln(x) ?
The solution to 3ln(x)-5ln(y)-1/4 ln(x) is ln((x^{11/4})/(y^5))