簡約 (1/2)^2-1/2-ln(1/2)

解

簡約

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

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

十進法表記

0.44314 \dots

解答ステップ

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

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

- (ln (1) - ln (2)) = ln (2)

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

2^{2} = 4

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

分数を組み合わせる

\frac{1}{4} - \frac{1}{2} : - \frac{1}{4}

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