簡約 ln((8x^2)/(3y))

解

簡約

ln (\frac{8 x ^{2}}{3 y})

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

解答ステップ

ln (\frac{8 x ^{2}}{3 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{8 x ^{2}}{3 y}) = ln (8 x^{2}) - ln (3 y)

= ln (8 x^{2}) - ln (3 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^{2}) = ln (8) + ln (x^{2}), ln (3 y) = ln (3) + ln (y)

= ln (8) + ln (x^{2}) - (ln (y) + ln (3))

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

ln (8) = 3 ln (2)

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

- (ln (3) + ln (y)) : - ln (3) - ln (y)

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