簡約-ln(7.8-3)+2ln(7.8-2)+C

解

簡約

- ln (7.8 - 3) + 2 ln (7.8 - 2) + C

ln (7.00833 \dots) + C

解答ステップ

- ln (7.8 - 3) + 2 ln (7.8 - 2) + C

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (7.8 - 2) = ln ((7.8 - 2)^{2})

= - ln (7.8 - 3) + ln ((7.8 - 2)^{2}) + C

対数の規則を適用する:

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

ln ((7.8 - 2)^{2}) - ln (7.8 - 3) = ln (\frac{( 7.8 - 2 ) ^{2}}{7.8 - 3})

= ln (\frac{( 7.8 - 2 ) ^{2}}{7.8 - 3}) + C

\frac{( 7.8 - 2 ) ^{2}}{7.8 - 3} = 7.00833 \dots

= ln (7.00833 \dots) + C