簡約-5/9 log_{2}(5/9)-4/9 log_{2}(4/9)

解

簡約

- \frac{5}{9} lo g_{2} (\frac{5}{9}) - \frac{4}{9} lo g_{2} (\frac{4}{9})

\frac{- 8 - lo g _{2} ( \frac{3125}{387420489} )}{9}

十進法表記

0.99107 \dots

解答ステップ

- \frac{5}{9} lo g_{2} (\frac{5}{9}) - \frac{4}{9} lo g_{2} (\frac{4}{9})

- \frac{5}{9} lo g_{2} (\frac{5}{9}) - \frac{4}{9} lo g_{2} (\frac{4}{9}) = \frac{- 5 lo g _{2} ( \frac{5}{9} ) - 4 lo g _{2} ( \frac{4}{9} )}{9}

= \frac{- 5 lo g _{2} ( \frac{5}{9} ) - 4 lo g _{2} ( \frac{4}{9} )}{9}

- 5 lo g_{2} (\frac{5}{9}) - 4 lo g_{2} (\frac{4}{9}) = - 8 - lo g_{2} (\frac{3125}{387420489})

= \frac{- 8 - lo g _{2} ( \frac{3125}{387420489} )}{9}