簡約 2000ln((140000)/(140000-2100(8)))-9.8(8)

解

簡約

2000 ln (\frac{140000}{140000 - 2100 ( 8 )}) - 9.8 (8)

2000 (ln (140000) - ln (123200)) - 78.4

十進法表記

177.26674 \dots

解答ステップ

2000 ln (\frac{140000}{140000 - 2100 ( 8 )}) - 9.8 (8)

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{140000}{140000 - 2100 ( 8 )}) = ln (140000) - ln (140000 - 2100 (8))

= 2000 (ln (140000) - ln (140000 - 2100 \cdot 8)) - 8 \cdot 9.8

ln (140000 - 2100 \cdot 8) = ln (123200)

= 2000 (ln (140000) - ln (123200)) - 8 \cdot 9.8

数を乗じる:

9.8 \cdot 8 = 78.4

= 2000 (ln (140000) - ln (123200)) - 78.4