簡約 ln(3/(8x^8y))

解

簡約

ln (\frac{3}{8 x ^{8} y})

ln (3) - 3 ln (2) - 8 ln (x) - ln (y)

解答ステップ

ln (\frac{3}{8 x ^{8} y})

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{3}{8 x ^{8} y}) = ln (3) - ln (8 x^{8} y)

= ln (3) - ln (8 x^{8} y)

対数の規則を適用する:

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

ln (8 x^{8} y) = ln (8) + ln (x^{8}) + ln (y)

= ln (3) - (ln (x^{8}) + ln (y) + ln (8))

対数の規則を適用する:

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

ln (x^{8}) = 8 ln (x)

= ln (3) - (ln (8) + 8 ln (x) + ln (y))

ln (8) = 3 ln (2)

= ln (3) - (8 ln (x) + ln (y) + 3 ln (2))

- (3 ln (2) + 8 ln (x) + ln (y)) : - 3 ln (2) - 8 ln (x) - ln (y)

= ln (3) - 3 ln (2) - 8 ln (x) - ln (y)