簡約 5ln((1-(sqrt(2))/2)/(1+(sqrt(2))/2))

解

簡約

5 ln (\frac{1 - \frac{2}{2}}{1 + \frac{2}{2}})

5 (ln (1 - \frac{2}{2}) - ln (1 + \frac{2}{2}))

十進法表記

- 8.81373 \dots

解答ステップ

5 ln (\frac{1 - \frac{2}{2}}{1 + \frac{2}{2}})

対数の規則を適用する:

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

ln (\frac{1 - \frac{2}{2}}{1 + \frac{2}{2}}) = ln (1 - \frac{2}{2}) - ln (1 + \frac{2}{2})

= 5 (ln (- \frac{2}{2} + 1) - ln (\frac{2}{2} + 1))