簡約-1/(sqrt(2))ln(1/(sqrt(2)))+1/(sqrt(2))

解

簡約

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

\frac{2}{4} ln (2) + \frac{2}{2}

十進法表記

0.95217 \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 2} ln (2)

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

規則を適用

- (- a) = a

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

ln (2) \frac{1}{2 2} = \frac{2}{4} ln (2)

\frac{1}{2} = \frac{2}{2}

= \frac{2}{4} ln (2) + \frac{2}{2}