化简-1/5 ln|x+1|+1/5 ln|x-4|+C

解答

化简

- \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ x - 4 ∣ + C

ln (5 \frac{∣ x - 4 ∣}{∣ x + 1 ∣}) + C

求解步骤

- \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ x - 4 ∣ + C

使用对数计算法则:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{5} ln ∣ x + 1 ∣ = ln (∣ x + 1 ∣^{\frac{1}{5}})

= - ln (∣ x + 1 ∣^{\frac{1}{5}}) + \frac{1}{5} ln ∣ x - 4 ∣ + C

使用对数计算法则:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{5} ln ∣ x - 4 ∣ = ln (∣ x - 4 ∣^{\frac{1}{5}})

= - ln (∣ x + 1 ∣^{\frac{1}{5}}) + ln (∣ x - 4 ∣^{\frac{1}{5}}) + C

使用对数计算法则:

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

ln (∣ x - 4 ∣^{\frac{1}{5}}) - ln (∣ x + 1 ∣^{\frac{1}{5}}) = ln (\frac{∣ x - 4 ∣ ^{\frac{1}{5}}}{∣ x + 1 ∣ ^{\frac{1}{5}}})

= ln (\frac{∣ x - 4 ∣ ^{\frac{1}{5}}}{∣ x + 1 ∣ ^{\frac{1}{5}}}) + C

合并相同指数项 :

\frac{x ^{\frac{a}{m}}}{y ^{\frac{b}{m}}} = m \frac{x ^{a}}{y ^{b}}

= ln (5 \frac{∣ x - 4 ∣}{∣ x + 1 ∣}) + C

s im pl i f y ln (\frac{1}{x}) - ln (2)

s im pl i f y \frac{1}{2} ln (\frac{1 + z}{1 - z})

s im pl i f y u (ln (u) - ln (x))

s im pl i f y lo g_{1.8} (\frac{8.13}{6.09}) + 52.11 - 52.34

s im pl i f y \frac{1}{4} ln (x) - \frac{1}{8} ln (x^{2} + 4)