簡約 ln((4x^2-x-2)/(x^2(x+1)))

解

簡約

ln (\frac{4 x ^{2} - x - 2}{x ^{2} ( x + 1 )})

ln (4 x^{2} - x - 2) - 2 ln (x) - ln (x + 1)

解答ステップ

ln (\frac{4 x ^{2} - x - 2}{x ^{2} ( x + 1 )})

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{4 x ^{2} - x - 2}{x ^{2} ( x + 1 )}) = ln (4 x^{2} - x - 2) - ln (x^{2} (x + 1))

= ln (4 x^{2} - x - 2) - ln (x^{2} (x + 1))

対数の規則を適用する:

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

ln (x^{2} (x + 1)) = ln (x^{2}) + ln (x + 1)

= ln (4 x^{2} - x - 2) - (ln (x^{2}) + ln (x + 1))

対数の規則を適用する:

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

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

= ln (4 x^{2} - x - 2) - (2 ln (x) + ln (x + 1))

- (2 ln (x) + ln (x + 1)) : - 2 ln (x) - ln (x + 1)

= ln (4 x^{2} - x - 2) - 2 ln (x) - ln (x + 1)