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

The solution to expand log_{4}(sqrt(3x^2y^4)) is log_{4}(x)+2log_{4}(y)+1/2 log_{4}(3)

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

expand

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

lo g_{4} (x) + 2 lo g_{4} (y) + \frac{1}{2} lo g_{4} (3)

Solution steps

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

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

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

Apply log rule:

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

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

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

Simplify

lo g_{4} (3) : \frac{1}{2} lo g_{4} (3)

= lo g_{4} (x y^{2}) + \frac{1}{2} lo g_{4} (3)

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

= lo g_{4} (x) + 2 lo g_{4} (y) + \frac{1}{2} lo g_{4} (3)

- ln 1 + cos^{2} (7.5)

\frac{8 x}{( x + 2 ) ( x - 2 )}

(λ - e^{- w} μ) (e^{w} - 1)

\frac{x - 4}{( x + 1 ) ( x + 2 )}

\frac{120 x ^{2}}{( 3 x + 5 ) ^{4}}

What is expand log_{4}(sqrt(3x^2y^4)) ?
The solution to expand log_{4}(sqrt(3x^2y^4)) is log_{4}(x)+2log_{4}(y)+1/2 log_{4}(3)