簡約 0.4log_{2}(0.4)+0.6log_{2}(0.6)

解

簡約

0.4 \cdot lo g_{2} (0.4) + 0.6 \cdot lo g_{2} (0.6)

lo g_{2} (0.51016 \dots)

十進法表記

- 0.97095 \dots

解答ステップ

0.4 lo g_{2} (0.4) + 0.6 lo g_{2} (0.6)

対数の規則を適用する:

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

0.4 lo g_{2} (0.4) = lo g_{2} (0. 4^{0.4})

= lo g_{2} (0. 4^{0.4}) + 0.6 lo g_{2} (0.6)

対数の規則を適用する:

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

0.6 lo g_{2} (0.6) = lo g_{2} (0. 6^{0.6})

= lo g_{2} (0. 4^{0.4}) + lo g_{2} (0. 6^{0.6})

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. 4^{0.4}) + lo g_{2} (0. 6^{0.6}) = lo g_{2} (0. 4^{0.4} \cdot 0. 6^{0.6})

= lo g_{2} (0. 4^{0.4} \cdot 0. 6^{0.6})

0. 4^{0.4} \cdot 0. 6^{0.6} = 0.51016 \dots

= lo g_{2} (0.51016 \dots)