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

解

簡約

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

20 (ln (1400) - ln (3400)) + 196

十進法表記

178.25393 \dots

解答ステップ

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

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 ( 20 )}) = ln (1400) - ln (1400 + 100 (20))

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

ln (1400 + 100 \cdot 20) = ln (3400)

= 20 (ln (1400) - ln (3400)) + 20 \cdot 9.8

数を乗じる:

9.8 \cdot 20 = 196

= 20 (ln (1400) - ln (3400)) + 196