簡約 ln((xsqrt(x+1))/(2e^4))

解

簡約

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

ln (x) + ln (x + 1) - ln (2) - 4

解答ステップ

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

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{x x + 1}{2 e ^{4}}) = ln (x x + 1) - ln (2 e^{4})

= ln (x x + 1) - ln (2 e^{4})

対数の規則を適用する:

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

ln (x x + 1) = ln (x) + ln (x + 1), ln (2 e^{4}) = ln (2) + ln (e^{4})

= ln (x) + ln (x + 1) - (ln (2) + ln (e^{4}))

対数の規則を適用する:

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

ln (e^{4}) = 4 ln (e)

= ln (x) + ln (x + 1) - (ln (2) + 4 ln (e))

4 ln (e) = 4

= ln (x) + ln (x + 1) - (ln (2) + 4)

- (ln (2) + 4) : - ln (2) - 4

= ln (x) + ln (x + 1) - ln (2) - 4