簡約 ln(x+1)+1/2 ln(2+3((y-1)/(x+1))^2)

解

簡約

ln (x + 1) + \frac{1}{2} ln (2 + 3 (\frac{y - 1}{x + 1})^{2})

ln (2 x^{2} + 4 x + 3 y^{2} + 5 - 6 y)

解答ステップ

ln (x + 1) + \frac{1}{2} ln (2 + 3 (\frac{y - 1}{x + 1})^{2})

対数の規則を適用する:

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

\frac{1}{2} ln (3 (\frac{y - 1}{x + 1})^{2} + 2) = ln (3 (\frac{y - 1}{x + 1})^{2} + 2)^{\frac{1}{2}}

= ln (x + 1) + ln (3 (\frac{y - 1}{x + 1})^{2} + 2)^{\frac{1}{2}}

対数の規則を適用する:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (x + 1) + ln (2 + 3 (\frac{y - 1}{x + 1})^{2})^{\frac{1}{2}} = ln (x + 1) (3 (\frac{y - 1}{x + 1})^{2} + 2)^{\frac{1}{2}}

= ln (x + 1) (3 (\frac{y - 1}{x + 1})^{2} + 2)^{\frac{1}{2}}

簡素化

(x + 1) (2 + 3 (\frac{y - 1}{x + 1})^{2})^{\frac{1}{2}} : 2 x^{2} + 4 x + 3 y^{2} + 5 - 6 y

= ln (2 x^{2} + 4 x + 3 y^{2} + 5 - 6 y)