簡約 2/5 ln|4w+1|+3/5 ln|w-1|

解

簡約

\frac{2}{5} ln ∣ 4 w + 1 ∣ + \frac{3}{5} ln ∣ w - 1 ∣

ln (∣ 4 w + 1 ∣^{\frac{2}{5}} ∣ w - 1 ∣^{\frac{3}{5}})

解答ステップ

\frac{2}{5} ln ∣ 4 w + 1 ∣ + \frac{3}{5} ln ∣ w - 1 ∣

対数の規則を適用する:

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

\frac{2}{5} ln ∣ 4 w + 1 ∣ = ln (∣ 4 w + 1 ∣^{\frac{2}{5}})

= ln (∣ 4 w + 1 ∣^{\frac{2}{5}}) + \frac{3}{5} ln ∣ w - 1 ∣

対数の規則を適用する:

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

\frac{3}{5} ln ∣ w - 1 ∣ = ln (∣ w - 1 ∣^{\frac{3}{5}})

= ln (∣ 4 w + 1 ∣^{\frac{2}{5}}) + ln (∣ w - 1 ∣^{\frac{3}{5}})

対数の規則を適用する:

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

ln (∣ 4 w + 1 ∣^{\frac{2}{5}}) + ln (∣ w - 1 ∣^{\frac{3}{5}}) = ln (∣ w - 1 ∣^{\frac{3}{5}} ∣ 4 w + 1 ∣^{\frac{2}{5}})

= ln (∣ 4 w + 1 ∣^{\frac{2}{5}} ∣ w - 1 ∣^{\frac{3}{5}})