簡約-(17/30)log_{2}(17/30)-(13/30)log_{2}(13/30)

解

簡約

- (\frac{17}{30}) lo g_{2} (\frac{17}{30}) - (\frac{13}{30}) lo g_{2} (\frac{13}{30})

- lo g_{2} (30 \frac{1 3 ^{13}}{3 0 ^{13}} 30 \frac{1 7 ^{17}}{3 0 ^{17}})

十進法表記

0.98713 \dots

解答ステップ

- (\frac{17}{30}) lo g_{2} (\frac{17}{30}) - (\frac{13}{30}) lo g_{2} (\frac{13}{30})

規則を適用する:

(a) = a

(\frac{17}{30}) = \frac{17}{30}

= - \frac{17}{30} lo g_{2} (\frac{17}{30}) - \frac{13}{30} lo g_{2} (\frac{13}{30})

- \frac{17}{30} lo g_{2} (\frac{17}{30}) = - lo g_{2} ((\frac{17}{30})^{\frac{17}{30}})

- \frac{13}{30} lo g_{2} (\frac{13}{30}) = - lo g_{2} ((\frac{13}{30})^{\frac{13}{30}})

= - lo g_{2} ((\frac{17}{30})^{\frac{17}{30}}) - lo g_{2} ((\frac{13}{30})^{\frac{13}{30}})

対数の規則を適用する:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

- lo g_{2} ((\frac{13}{30})^{\frac{13}{30}}) - lo g_{2} ((\frac{17}{30})^{\frac{17}{30}}) = lo g_{2} ((\frac{13}{30})^{\frac{13}{30}} (\frac{17}{30})^{\frac{17}{30}})

= - lo g_{2} ((\frac{13}{30})^{\frac{13}{30}} (\frac{17}{30})^{\frac{17}{30}})

(\frac{13}{30})^{\frac{13}{30}} (\frac{17}{30})^{\frac{17}{30}} = 30 \frac{1 3 ^{13}}{3 0 ^{13}} 30 \frac{1 7 ^{17}}{3 0 ^{17}}

= - lo g_{2} (30 \frac{1 3 ^{13}}{3 0 ^{13}} 30 \frac{1 7 ^{17}}{3 0 ^{17}})