簡約 0.01log_{2}(0.01)+0.99log_{2}(0.99)

解

簡約

0.01 \cdot lo g_{2} (0.01) + 0.99 \cdot lo g_{2} (0.99)

lo g_{2} (0.94553 \dots)

十進法表記

- 0.08079 \dots

解答ステップ

0.01 lo g_{2} (0.01) + 0.99 lo g_{2} (0.99)

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.01 lo g_{2} (0.01) = lo g_{2} (0.0 1^{0.01})

= lo g_{2} (0.0 1^{0.01}) + 0.99 lo g_{2} (0.99)

対数の規則を適用する:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.99 lo g_{2} (0.99) = lo g_{2} (0.9 9^{0.99})

= lo g_{2} (0.0 1^{0.01}) + lo g_{2} (0.9 9^{0.99})

対数の規則を適用する:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{2} (0.0 1^{0.01}) + lo g_{2} (0.9 9^{0.99}) = lo g_{2} (0.0 1^{0.01} \cdot 0.9 9^{0.99})

= lo g_{2} (0.0 1^{0.01} \cdot 0.9 9^{0.99})

0.0 1^{0.01} \cdot 0.9 9^{0.99} = 0.94553 \dots

= lo g_{2} (0.94553 \dots)