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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

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

lo g_{10} (\frac{1}{a})

\frac{2}{3} lo g_{3} (2 x - 5) - 5 lo g_{3} (4 x + 2)

- \frac{ln ( 2 )}{5 ln ( 3 )}

ln (x^{5}) - ln (x^{3})

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