簡約-(3/4)log_{2}(3/4)-((1/4)log_{2}(1/4))

解

簡約

- (\frac{3}{4}) lo g_{2} (\frac{3}{4}) - ((\frac{1}{4}) lo g_{2} (\frac{1}{4}))

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

十進法表記

0.81127 \dots

解答ステップ

- (\frac{3}{4}) lo g_{2} (\frac{3}{4}) - ((\frac{1}{4}) lo g_{2} (\frac{1}{4}))

規則を適用する:

- (a) = - a

- ((\frac{1}{4}) lo g_{2} (\frac{1}{4})) = - (\frac{1}{4}) lo g_{2} (\frac{1}{4})

= - \frac{3}{4} lo g_{2} (\frac{3}{4}) - \frac{1}{4} lo g_{2} (\frac{1}{4})

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

\frac{1}{4} lo g_{2} (\frac{1}{4}) = - \frac{1}{2}

= - \frac{3}{4} (lo g_{2} (3) - 2) - (- \frac{1}{2})

拡張

- \frac{3}{4} (lo g_{2} (3) - 2) - (- \frac{1}{2}) : - \frac{3}{4} lo g_{2} (3) + \frac{4}{2}

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

数を割る:

\frac{4}{2} = 2

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