What is expand log_{1/2}(sqrt(xy)) ?

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

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expand log_{1/2}(sqrt(xy))

expand

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

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

Solution steps

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

Rewrite as

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

Apply log rule

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

assuming

x \geq 0

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

Simplify

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

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

Remove parentheses:

(- a) = - a

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

x (y = 2 x^{2} + 4 x - 6)

\frac{1}{( s ^{2} + 4 ) ^{3}}

(e^{t i} + e^{- t i})^{3}

(n^{2} + n + 5)^{10}

f_{x} (1, - 2)

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