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

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

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

expand

lo g_{2} (4 a c)

\frac{1}{2} lo g_{2} (a c) + 1

Solution steps

lo g_{2} (4 a c)

4 a c = 2 a c

= lo g_{2} (2 a c)

Apply log rule:

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

lo g_{2} (2 a c) = lo g_{2} (a c) + lo g_{2} (2)

= lo g_{2} (a c) + lo g_{2} (2)

Simplify

lo g_{2} (2) : 1

Rewrite as

= lo g_{2} ((a c)^{\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} (a c) + 1

(y + x^{2} + y^{2}) d x - x d y

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

(\frac{x ^{4}}{2} + \frac{4}{3 x ^{2}})^{12}

(2 x + 3 y - 7) d x + (- 3 x - 2 y - 4) d y

\frac{1}{4 s t ( 1 + s ) ( 1 + t )}

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