簡約 ln(1/(16e^2))

解

簡約

ln (\frac{1}{16 e ^{2}})

- (4 ln (2) + 2)

十進法表記

- 4.77258 \dots

解答ステップ

ln (\frac{1}{16 e ^{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{1}{16 e ^{2}}) = ln (1) - ln (16 e^{2})

= ln (1) - ln (16 e^{2})

対数の規則を適用する:

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

ln (16 e^{2}) = ln (16) + ln (e^{2})

= ln (1) - (ln (16) + ln (e^{2}))

対数の規則を適用する:

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

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

= ln (1) - (ln (16) + 2 ln (e))

ln (1) = 0

- (ln (16) + 2 ln (e)) = - (4 ln (2) + 2)

= 0 - (4 ln (2) + 2)

0 - (4 ln (2) + 2) = - (4 ln (2) + 2)

= - (4 ln (2) + 2)