展开 ln(\sqrt[3]{p^2q})

解答

展开

ln (3 p^{2} q)

\frac{1}{3} ln (q) + \frac{2}{3} ln (p)

求解步骤

ln (3 p^{2} q)

改写为

= ln ((p^{2} q)^{\frac{1}{3}})

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}{3} ln (p^{2} q)

化简

ln (p^{2} q) : 2 ln (p) + ln (q)

= \frac{1}{3} (2 ln (p) + ln (q))

使用分配律:

a (b + c) = ab + a c

a = \frac{1}{3}, b = ln (q), c = 2 ln (p)

= \frac{1}{3} ln (q) + \frac{1}{3} \cdot 2 ln (p)

= \frac{1}{3} ln (q) + 2 \cdot \frac{1}{3} ln (p)

2 \cdot \frac{1}{3} ln (p) = \frac{2}{3} ln (p)

= \frac{1}{3} ln (q) + \frac{2}{3} ln (p)

e x p an d e^{3 x} (e^{3 x} + 3 x e^{3 x})

s im pl i f y 3 (3 + x)

e x p an d \frac{1}{( s - 1 ) ^{4}}

e x p an d (x + \frac{1}{2}) (x - 0) (x - \frac{1}{2})

s im pl i f y \frac{2 ( x ^{2} - 4 )}{3 3 x} + 2 x^{\frac{5}{3}}