What is expand log_{2}(sqrt(4xy)) ?

The solution to expand log_{2}(sqrt(4xy)) is 1/2 log_{2}(xy)+1

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expand log_{2}(sqrt(4xy))

expand

lo g_{2} (4 x y)

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

Solution steps

lo g_{2} (4 x y)

4 x y = 2 x y

= lo g_{2} (2 x y)

Apply log rule:

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

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

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

Simplify

lo g_{2} (2) : 1

Rewrite as

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

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

\frac{n}{2 ^{n} ( n + 1 )}

(3 x + sin (y)) d y

4 y^{2} \cdot (4 y y^{'} (t) - 1)

(\frac{2}{3} a - \frac{1}{3} b)^{2}

(x - \frac{1}{a}) (x - \frac{1}{b}) (x - \frac{1}{c})

What is expand log_{2}(sqrt(4xy)) ?
The solution to expand log_{2}(sqrt(4xy)) is 1/2 log_{2}(xy)+1