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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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Frequently Asked Questions (FAQ)

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