簡約 ln((e^3x^3sqrt(x+2))/(3y^2))

解

簡約

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

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

解答ステップ

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

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

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

対数の規則を適用する:

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

ln (e^{3}) = 3 ln (e)

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

対数の規則を適用する:

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

ln (x^{3}) = 3 ln (x)

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

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)

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

3 ln (e) = 3

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

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

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