簡約-(3/5)log_{2}(3/5)-(2/5)log_{2}(2/5)

解

簡約

- (\frac{3}{5}) lo g_{2} (\frac{3}{5}) - (\frac{2}{5}) lo g_{2} (\frac{2}{5})

- lo g_{2} (5 \frac{4}{25} 5 \frac{27}{125})

十進法表記

0.97095 \dots

解答ステップ

- (\frac{3}{5}) lo g_{2} (\frac{3}{5}) - (\frac{2}{5}) lo g_{2} (\frac{2}{5})

規則を適用する:

(a) = a

(\frac{3}{5}) = \frac{3}{5}

= - \frac{3}{5} lo g_{2} (\frac{3}{5}) - \frac{2}{5} lo g_{2} (\frac{2}{5})

- \frac{3}{5} lo g_{2} (\frac{3}{5}) = - lo g_{2} ((\frac{3}{5})^{\frac{3}{5}})

- \frac{2}{5} lo g_{2} (\frac{2}{5}) = - lo g_{2} ((\frac{2}{5})^{\frac{2}{5}})

= - lo g_{2} ((\frac{3}{5})^{\frac{3}{5}}) - lo g_{2} ((\frac{2}{5})^{\frac{2}{5}})

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{2}{5})^{\frac{2}{5}}) - lo g_{2} ((\frac{3}{5})^{\frac{3}{5}}) = lo g_{2} ((\frac{2}{5})^{\frac{2}{5}} (\frac{3}{5})^{\frac{3}{5}})

= - lo g_{2} ((\frac{2}{5})^{\frac{2}{5}} (\frac{3}{5})^{\frac{3}{5}})

(\frac{2}{5})^{\frac{2}{5}} (\frac{3}{5})^{\frac{3}{5}} = 5 \frac{4}{25} 5 \frac{27}{125}

= - lo g_{2} (5 \frac{4}{25} 5 \frac{27}{125})