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

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

Popular >

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

Apply log rule:

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

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

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

2 ln (e) + 2 lo g_{x} (+ 3 lo g_{y} (x))

ln (\frac{1}{π})

\frac{1}{2} ln (- 3)

ln (- 23)

ln (\frac{( 30 )}{( 21.001 )})

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