簡約 (-4/6)log_{2}(4/6)-(2/6)log_{2}(2/6)

解

簡約

(- \frac{4}{6}) lo g_{2} (\frac{4}{6}) - (\frac{2}{6}) lo g_{2} (\frac{2}{6})

lo g_{2} (\frac{3}{3 4})

十進法表記

0.91829 \dots

解答ステップ

(- \frac{4}{6}) lo g_{2} (\frac{4}{6}) - (\frac{2}{6}) lo g_{2} (\frac{2}{6})

(- \frac{4}{6}) lo g_{2} (\frac{4}{6}) = lo g_{2} ((\frac{4}{6})^{- \frac{4}{6}})

- (\frac{2}{6}) lo g_{2} (\frac{2}{6}) = - lo g_{2} ((\frac{2}{6})^{\frac{2}{6}})

= lo g_{2} ((\frac{4}{6})^{- \frac{4}{6}}) - lo g_{2} ((\frac{2}{6})^{\frac{2}{6}})

対数の規則を適用する:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{2} ((\frac{4}{6})^{- \frac{4}{6}}) - lo g_{2} ((\frac{2}{6})^{\frac{2}{6}}) = lo g_{2} \frac{( \frac{4}{6} ) ^{- \frac{4}{6}}}{( \frac{2}{6} ) ^{\frac{2}{6}}}

= lo g_{2} \frac{( \frac{4}{6} ) ^{- \frac{4}{6}}}{( \frac{2}{6} ) ^{\frac{2}{6}}}

\frac{( \frac{4}{6} ) ^{- \frac{4}{6}}}{( \frac{2}{6} ) ^{\frac{2}{6}}} = \frac{3}{3 4}

= lo g_{2} (\frac{3}{3 4})