展开 log_{10}(\sqrt[5]{(x+2)/(x^3(x^2+4))})

解答

展开

lo g_{10} (5 \frac{x + 2}{x ^{3} ( x ^{2} + 4 )})

\frac{1}{5} lo g_{10} (\frac{x + 2}{x ^{5} + 4 x ^{3}})

求解步骤

lo g_{10} (5 \frac{x + 2}{x ^{3} ( x ^{2} + 4 )})

5 \frac{x + 2}{x ^{3} ( x ^{2} + 4 )} = 5 \frac{x + 2}{x ^{5} + 4 x ^{3}}

= lo g_{10} (5 \frac{x + 2}{x ^{5} + 4 x ^{3}})

改写为

= lo g_{10} ((\frac{x + 2}{x ^{5} + 4 x ^{3}})^{\frac{1}{5}})

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}{5} lo g_{10} (\frac{x + 2}{x ^{5} + 4 x ^{3}})

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

e x p an d \frac{\frac{d}{d x} ( 3 )}{2 ( 2 x ^{4} + 5 x ^{2} + 3 ) ^{4}}

e x p an d \frac{3}{4} (3 - \frac{x}{9}) - \frac{1}{6} (1 - \frac{x}{3} = 1 - (x - \frac{3}{2}))

s im pl i f y (2 + 3 x i)^{2}

e x p an d \frac{5 x + 31}{( x + 2 ) ( x + 5 )}