簡約 1/2 ln((sqrt(3))/4)-1/2 ln(1/2)

解

簡約

\frac{1}{2} ln (\frac{3}{4}) - \frac{1}{2} ln (\frac{1}{2})

ln (\frac{4 3 2}{2})

十進法表記

- 0.07192 \dots

解答ステップ

\frac{1}{2} ln (\frac{3}{4}) - \frac{1}{2} ln (\frac{1}{2})

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{3}{4}) = ln (\frac{3}{4})^{\frac{1}{2}}

= ln (\frac{3}{4})^{\frac{1}{2}} - \frac{1}{2} ln (\frac{1}{2})

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

= ln (\frac{3}{4})^{\frac{1}{2}} - ln ((\frac{1}{2})^{\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{3}{4})^{\frac{1}{2}} - ln ((\frac{1}{2})^{\frac{1}{2}}) = ln \frac{( \frac{3}{4} ) ^{\frac{1}{2}}}{( \frac{1}{2} ) ^{\frac{1}{2}}}

= ln \frac{( \frac{3}{4} ) ^{\frac{1}{2}}}{( \frac{1}{2} ) ^{\frac{1}{2}}}

\frac{( \frac{3}{4} ) ^{\frac{1}{2}}}{( \frac{1}{2} ) ^{\frac{1}{2}}} = \frac{4 3 2}{2}

= ln (\frac{4 3 2}{2})