展开 log_{1/2}(sqrt(xy))

解答

展开

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

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

求解步骤

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

改写为

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

使用对数运算法则:

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

假定

x \geq 0

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

化简

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

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

去除括号:

(- a) = - a

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

e x p an d x (y = 2 x^{2} + 4 x - 6)

e x p an d \frac{1}{( s ^{2} + 4 ) ^{3}}

s im pl i f y (e^{t i} + e^{- t i})^{3}

e x p an d (n^{2} + n + 5)^{10}

e x p an d f_{x} (1, - 2)