展開する ln(sqrt(6x^9y^5))

解

展開する

ln (6 x^{9} y^{5})

2 ln (x^{2} y) + \frac{1}{2} ln (x y) + \frac{1}{2} ln (6)

解答ステップ

ln (6 x^{9} y^{5})

6 x^{9} y^{5} = 6 x^{4} y^{2} x y

= ln (6 x^{4} y^{2} x y)

対数の規則を適用する:

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

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

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

簡素化

ln (6) : \frac{1}{2} ln (6)

= ln (x^{4} y^{2} x y) + \frac{1}{2} ln (6)

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

= 2 (2 ln (x) + ln (y)) + \frac{1}{2} ln (x y) + \frac{1}{2} ln (6)

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

= 2 ln (x^{2} y) + \frac{1}{2} ln (x y) + \frac{1}{2} ln (6)

簡素化

ln (x^{2} y) : 2 ln (x) + ln (y)

= 2 (2 ln (x) + ln (y)) + \frac{1}{2} ln (x y) + \frac{1}{2} ln (6)

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

= 2 ln (x^{2} y) + \frac{1}{2} ln (x y) + \frac{1}{2} ln (6)