簡約-1ln((s^2-a^2)/(s^2))

解

簡約

- 1 ln (\frac{s ^{2} - a ^{2}}{s ^{2}})

- ln (s^{2} - a^{2}) + 2 ln (s)

解答ステップ

- 1 \cdot ln (\frac{s ^{2} - a ^{2}}{s ^{2}})

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{s ^{2} - a ^{2}}{s ^{2}}) = ln (s^{2} - a^{2}) - ln (s^{2})

= - 1 \cdot (ln (s^{2} - a^{2}) - ln (s^{2}))

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (s^{2}) = 2 ln (s)

= - 1 \cdot (ln (s^{2} - a^{2}) - 2 ln (s))

乗算:

1 \cdot (ln (s^{2} - a^{2}) - 2 ln (s)) = (ln (s^{2} - a^{2}) - 2 ln (s))

= - (ln (s^{2} - a^{2}) - 2 ln (s))

括弧を分配する

= - (ln (s^{2} - a^{2})) - (- 2 ln (s))

マイナス・プラスの規則を適用する

- (- a) = a, - (a) = - a

= - ln (s^{2} - a^{2}) + 2 ln (s)