簡約 ln((4x)/(7y^2))

解

簡約

ln (\frac{4 x}{7 y ^{2}})

2 ln (2) + ln (x) - ln (7) - 2 ln (y)

解答ステップ

ln (\frac{4 x}{7 y ^{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{4 x}{7 y ^{2}}) = ln (4 x) - ln (7 y^{2})

= ln (4 x) - ln (7 y^{2})

対数の規則を適用する:

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

ln (4 x) = ln (4) + ln (x), ln (7 y^{2}) = ln (7) + ln (y^{2})

= ln (4) + ln (x) - (ln (y^{2}) + ln (7))

対数の規則を適用する:

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

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

= ln (4) + ln (x) - (ln (7) + 2 ln (y))

ln (4) = 2 ln (2)

= 2 ln (2) + ln (x) - (2 ln (y) + ln (7))

- (ln (7) + 2 ln (y)) : - ln (7) - 2 ln (y)

= 2 ln (2) + ln (x) - ln (7) - 2 ln (y)