簡約-0.1log_{2}(0.1)-0.9log_{2}(0.9)

解

簡約

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

- lo g_{2} (0.72246 \dots)

十進法表記

0.46899 \dots

解答ステップ

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

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. 1^{0.1}) - 0.9 lo g_{2} (0.9)

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

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

を書き換え

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

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

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

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

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

= - lo g_{2} (0.72246 \dots)