What is log_{4}(sqrt(3x^2y^4)) ?

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

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simplify log_{4}(sqrt(3x^2y^4))

simplify

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

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

Solution steps

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

Simplify

3 x^{2} y^{4} : 3 x y^{2}

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

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

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

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

Simplify

lo g_{4} (y^{2}) : lo g_{2} (y)

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

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