What is 1/3 ln(x)+2/3 ln(y) ?

The solution to 1/3 ln(x)+2/3 ln(y) is ln(x^{1/3}y^{2/3})

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simplify 1/3 ln(x)+2/3 ln(y)

simplify

\frac{1}{3} ln (x) + \frac{2}{3} ln (y)

ln (x^{\frac{1}{3}} y^{\frac{2}{3}})

Solution steps

\frac{1}{3} ln (x) + \frac{2}{3} ln (y)

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{2}{3} ln (y)

Apply log rule:

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

\frac{2}{3} ln (y) = ln (y^{\frac{2}{3}})

= ln (x^{\frac{1}{3}}) + ln (y^{\frac{2}{3}})

Apply log rule:

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

ln (x^{\frac{1}{3}}) + ln (y^{\frac{2}{3}}) = ln (x^{\frac{1}{3}} y^{\frac{2}{3}})

= ln (x^{\frac{1}{3}} y^{\frac{2}{3}})

lo g_{b} (\frac{A}{10})

2 ln (3) - 3 ln (3) + 2 ln (5)

2 ln (\frac{π}{3})

ln (\frac{w ^{5} x ^{\frac{4}{5}}}{y ^{8} z ^{7}})

What is 1/3 ln(x)+2/3 ln(y) ?
The solution to 1/3 ln(x)+2/3 ln(y) is ln(x^{1/3}y^{2/3})