What is 2/3 log_{4}(x)+log_{4}(y) ?

The solution to 2/3 log_{4}(x)+log_{4}(y) is log_{4}(x^{2/3}y)

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simplify 2/3 log_{4}(x)+log_{4}(y)

simplify

\frac{2}{3} lo g_{4} (x) + lo g_{4} (y)

lo g_{4} (x^{\frac{2}{3}} y)

Solution steps

\frac{2}{3} lo g_{4} (x) + lo g_{4} (y)

Apply log rule:

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

\frac{2}{3} lo g_{4} (x) = lo g_{4} (x^{\frac{2}{3}})

= lo g_{4} (x^{\frac{2}{3}}) + lo g_{4} (y)

Apply log rule:

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

lo g_{4} (x^{\frac{2}{3}}) + lo g_{4} (y) = lo g_{4} (y x^{\frac{2}{3}})

= lo g_{4} (x^{\frac{2}{3}} y)

ln (x) - ln (10)

lo g_{3} (\frac{w}{9})

lo g_{w} (\frac{9 x}{4})

ln (x) - ln (16)

What is 2/3 log_{4}(x)+log_{4}(y) ?
The solution to 2/3 log_{4}(x)+log_{4}(y) is log_{4}(x^{2/3}y)