簡約 ln(2/(sqrt(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)

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

共通項をくくり出す

ln (2)

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

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

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