簡約 ln(1/2)-1/2 ln((1/2)^2+1)

解

簡約

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

ln (\frac{5}{5})

十進法表記

- 0.80471 \dots

解答ステップ

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

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

対数の規則を適用する:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

\frac{\frac{1}{2}}{( ( \frac{1}{2} ) ^{2} + 1 ) ^{\frac{1}{2}}} = \frac{5}{5}

= ln (\frac{5}{5})