簡約 20ln((1400)/(1400+100(25)))+9.8(25)

解

簡約

20 ln (\frac{1400}{1400 + 100 ( 25 )}) + 9.8 (25)

20 (ln (1400) - ln (3900)) + 245

十進法表記

224.50991 \dots

解答ステップ

20 ln (\frac{1400}{1400 + 100 ( 25 )}) + 9.8 (25)

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{1400}{1400 + 100 ( 25 )}) = ln (1400) - ln (1400 + 100 (25))

= 20 (ln (1400) - ln (1400 + 100 \cdot 25)) + 25 \cdot 9.8

ln (1400 + 100 \cdot 25) = ln (3900)

= 20 (ln (1400) - ln (3900)) + 25 \cdot 9.8

数を乗じる:

9.8 \cdot 25 = 245

= 20 (ln (1400) - ln (3900)) + 245