What is 1/3 log_{2}(x)+2/3 log_{2}(y)-3 ?

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

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simplify 1/3 log_{2}(x)+2/3 log_{2}(y)-3

simplify

\frac{1}{3} lo g_{2} (x) + \frac{2}{3} lo g_{2} (y) - 3

lo g_{2} (x^{\frac{1}{3}} y^{\frac{2}{3}}) - 3

Solution steps

\frac{1}{3} lo g_{2} (x) + \frac{2}{3} lo g_{2} (y) - 3

Apply log rule:

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

\frac{1}{3} lo g_{2} (x) = lo g_{2} (x^{\frac{1}{3}})

= lo g_{2} (x^{\frac{1}{3}}) + \frac{2}{3} lo g_{2} (y) - 3

Apply log rule:

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

\frac{2}{3} lo g_{2} (y) = lo g_{2} (y^{\frac{2}{3}})

= lo g_{2} (x^{\frac{1}{3}}) + lo g_{2} (y^{\frac{2}{3}}) - 3

Apply log rule:

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

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

= lo g_{2} (x^{\frac{1}{3}} y^{\frac{2}{3}}) - 3

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