簡約-5/9 (ln(10-0.9v^2)-ln(10-0.9v_{0}^2))

解

簡約

- \frac{5}{9} (ln (10 - 0.9 v^{2}) - ln (10 - 0.9 v_{0}^{2}))

- \frac{5}{9} ln (\frac{10 - 0.9 v ^{2}}{10 - 0.9 v _{0}^{2}})

解答ステップ

- \frac{5}{9} (ln (10 - 0.9 v^{2}) - ln (10 - 0.9 v_{0}^{2}))

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 (10 - 0.9 v^{2}) - ln (10 - 0.9 v_{0}^{2}) = ln (\frac{- 0.9 v ^{2} + 10}{- 0.9 v _{0}^{2} + 10})

= - \frac{5}{9} ln (\frac{10 - 0.9 v ^{2}}{10 - 0.9 v _{0}^{2}})