簡約 1/5 ln(x+1)+4/5 ln(x-4)

解

簡約

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

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

解答ステップ

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

対数の規則を適用する:

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{4}{5} ln (x - 4)

対数の規則を適用する:

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

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

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

対数の規則を適用する:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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