What is ln(x^{1/3}y^{1/2}) ?

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

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simplify ln(x^{1/3}y^{1/2})

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

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