簡約 2ln(3)-1/2 ln(2)+pi/(12)

解

簡約

2 ln (3) - \frac{1}{2} ln (2) + \frac{π}{12}

ln (\frac{9 2}{2}) + \frac{π}{12}

十進法表記

2.11245 \dots

解答ステップ

2 ln (3) - \frac{1}{2} ln (2) + \frac{π}{12}

対数の規則を適用する:

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

2 ln (3) = ln (3^{2})

= ln (3^{2}) - \frac{1}{2} ln (2) + \frac{π}{12}

対数の規則を適用する:

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

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

= ln (3^{2}) - ln (2^{\frac{1}{2}}) + \frac{π}{12}

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

= ln (\frac{3 ^{2}}{2 ^{\frac{1}{2}}}) + \frac{π}{12}

\frac{3 ^{2}}{2 ^{\frac{1}{2}}} = \frac{9 2}{2}

= ln (\frac{9 2}{2}) + \frac{π}{12}