化简 x/(ln(x))(ln(x)-ln(x^3))

解答

化简

\frac{x}{ln ( x )} (ln (x) - ln (x^{3}))

- \frac{x ln ( x ^{2} )}{ln ( x )}

求解步骤

\frac{x}{ln ( x )} (ln (x) - ln (x^{3}))

使用对数计算法则:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x) - ln (x^{3}) = ln (\frac{x}{x ^{3}})

= \frac{x}{ln ( x )} ln (\frac{x}{x ^{3}})

约分:

x

= \frac{x}{ln ( x )} ln (\frac{1}{x ^{2}})

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ln ( \frac{1}{x ^{2}} )}{ln ( x )}

化简

ln (\frac{1}{x ^{2}}) : - ln (x^{2})

= \frac{x ( - ln ( x ^{2} ) )}{ln ( x )}

去除括号:

(- a) = - a

= \frac{- x ln ( x ^{2} )}{ln ( x )}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{x ln ( x ^{2} )}{ln ( x )}

s im pl i f y - lo g_{10} (2.8 \cdot 1 0^{- 4})

s im pl i f y 5 lo g_{10} (x) + 3 lo g_{10} (y)

s im pl i f y lo g_{3} (x) + 4 lo g_{3} (y)

s im pl i f y \frac{1}{3} ln ∣ y - 1 ∣ - \frac{1}{3} ln ∣ y + 2 ∣

s im pl i f y ln (20) + 2 ln (\frac{1}{2}) + \frac{1}{3} ln (27)