簡約 ln(C/((b^2+(x-a)^2)^2))

解

簡約

ln \frac{C}{( b ^{2} + ( x - a ) ^{2} ) ^{2}}

ln (C) - 2 ln (b^{2} + (x - a)^{2})

解答ステップ

ln \frac{C}{( b ^{2} + ( x - a ) ^{2} ) ^{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{C}{( b ^{2} + ( x - a ) ^{2} ) ^{2}} = ln (C) - ln ((b^{2} + (x - a)^{2})^{2})

= ln (C) - ln ((b^{2} + (x - a)^{2})^{2})

対数の規則を適用する:

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

ln ((b^{2} + (x - a)^{2})^{2}) = 2 ln (b^{2} + (x - a)^{2})

= ln (C) - 2 ln (b^{2} + (x - a)^{2})