簡約 0.9log_{2}(0.9)+0.1log_{2}(0.1)

解

簡約

0.9 \cdot lo g_{2} (0.9) + 0.1 \cdot lo g_{2} (0.1)

lo g_{2} (0.72246 \dots)

十進法表記

- 0.46899 \dots

解答ステップ

0.9 lo g_{2} (0.9) + 0.1 lo g_{2} (0.1)

対数の規則を適用する:

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

0.9 lo g_{2} (0.9) = lo g_{2} (0. 9^{0.9})

= lo g_{2} (0. 9^{0.9}) + 0.1 lo g_{2} (0.1)

対数の規則を適用する:

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

0.1 lo g_{2} (0.1) = lo g_{2} (0. 1^{0.1})

= lo g_{2} (0. 9^{0.9}) + lo g_{2} (0. 1^{0.1})

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. 9^{0.9}) + lo g_{2} (0. 1^{0.1}) = lo g_{2} (0. 9^{0.9} \cdot 0. 1^{0.1})

= lo g_{2} (0. 9^{0.9} \cdot 0. 1^{0.1})

0. 9^{0.9} \cdot 0. 1^{0.1} = 0.72246 \dots

= lo g_{2} (0.72246 \dots)