簡約-(7/9 log_{2}(7/9)+2/9 log_{2}(2/9))

解

簡約

- (\frac{7}{9} lo g_{2} (\frac{7}{9}) + \frac{2}{9} lo g_{2} (\frac{2}{9}))

- \frac{lo g _{2} ( \frac{3294172}{387420489} )}{9}

十進法表記

0.76420 \dots

解答ステップ

- (\frac{7}{9} lo g_{2} (\frac{7}{9}) + \frac{2}{9} lo g_{2} (\frac{2}{9}))

\frac{7}{9} lo g_{2} (\frac{7}{9}) + \frac{2}{9} lo g_{2} (\frac{2}{9}) = \frac{7 lo g _{2} ( \frac{7}{9} ) + 2 lo g _{2} ( \frac{2}{9} )}{9}

= - \frac{7 lo g _{2} ( \frac{7}{9} ) + 2 lo g _{2} ( \frac{2}{9} )}{9}

7 lo g_{2} (\frac{7}{9}) + 2 lo g_{2} (\frac{2}{9}) = lo g_{2} (\frac{3294172}{387420489})

= - \frac{lo g _{2} ( \frac{3294172}{387420489} )}{9}