簡約 ln((sqrt(2))/2)-ln(1)

解

簡約

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

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

十進法表記

- 0.34657 \dots

解答ステップ

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

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 (1)

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

ln (1) = 0

= \frac{1}{2} ln (2) - ln (2) - 0

類似した元を足す:

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

= - \frac{1}{2} ln (2) - 0

- \frac{1}{2} ln (2) - 0 = - \frac{1}{2} ln (2)

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