簡約-1/2 ln(1/2)+1/2

解

簡約

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

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

十進法表記

0.84657 \dots

解答ステップ

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

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

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

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

規則を適用

- (- a) = a

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