簡約 ln(1/2)*ln(1/2)

解

簡約

ln (\frac{1}{2}) \cdot ln (\frac{1}{2})

ln^{2} (2)

十進法表記

0.48045 \dots

解答ステップ

ln (\frac{1}{2}) ln (\frac{1}{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}{2}) = ln (1) - ln (2)

= ln (\frac{1}{2}) (ln (1) - ln (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}{2}) = ln (1) - ln (2)

= (ln (1) - ln (2)) (ln (1) - ln (2))

簡素化

(ln (1) - ln (2)) (ln (1) - ln (2)) : (ln (1) - ln (2))^{2}

対数の規則を適用する:

lo g_{a} (1) = 0

= (0 - ln (2))^{2}

0 - ln (2) = - ln (2)

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

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

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

= ln^{2} (2)