簡約 25ln(e 2/5)

解

簡約

25 ln (e \frac{2}{5})

25 + 25 (ln (2) - ln (5))

十進法表記

2.09273 \dots

解答ステップ

25 ln (e \frac{2}{5})

対数の規則を適用する:

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

25 ln (e \frac{2}{5}) = 25 ln (e) + 25 ln (\frac{2}{5})

= 25 ln (e) + 25 ln (\frac{2}{5})

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{2}{5}) = ln (2) - ln (5)

= 25 ln (e) + 25 (ln (2) - ln (5))

25 ln (e) = 25

= 25 + 25 (ln (2) - ln (5))