簡約 2/3 ln((e^2+1)(e+1)(e-1)(e^8+e^4+1))

解

簡約

\frac{2}{3} ln ((e^{2} + 1) (e + 1) (e - 1) (e^{8} + e^{4} + 1))

\frac{2}{3} ln (e^{2} + 1) + \frac{2}{3} ln (e + 1) + \frac{2}{3} ln (e - 1) + \frac{2}{3} ln (e^{8} + e^{4} + 1)

十進法表記

7.99999 \dots

解答ステップ

\frac{2}{3} ln ((e^{2} + 1) (e + 1) (e - 1) (e^{8} + e^{4} + 1))

対数の規則を適用する:

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

\frac{2}{3} ln ((e^{2} + 1) (e + 1) (e - 1) (e^{8} + e^{4} + 1)) = \frac{2}{3} ln (e^{2} + 1) + \frac{2}{3} ln (e + 1) + \frac{2}{3} ln (e - 1) + \frac{2}{3} ln (e^{8} + e^{4} + 1)

= \frac{2}{3} ln (e^{2} + 1) + \frac{2}{3} ln (e + 1) + \frac{2}{3} ln (e - 1) + \frac{2}{3} ln (e^{8} + e^{4} + 1)