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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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Frequently Asked Questions (FAQ)

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