簡約 ln((sqrt(2))/2)

解

簡約

ln (\frac{2}{2})

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

十進法表記

- 0.34657 \dots

解答ステップ

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

= ln (2) - ln (2)

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

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

共通項をくくり出す

ln (2)

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

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

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