簡約 ln((x^2+5x+6)/((x+3)(x-2)))

解

簡約

ln (\frac{x ^{2} + 5 x + 6}{( x + 3 ) ( x - 2 )})

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

解答ステップ

ln (\frac{x ^{2} + 5 x + 6}{( x + 3 ) ( x - 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{x ^{2} + 5 x + 6}{( x + 3 ) ( x - 2 )}) = ln (x^{2} + 5 x + 6) - ln ((x + 3) (x - 2))

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

対数の規則を適用する:

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

ln ((x + 3) (x - 2)) = ln (x + 3) + ln (x - 2)

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

- (ln (x + 3) + ln (x - 2)) : - ln (x + 3) - ln (x - 2)

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