簡約 0.4log_{2}(1/(0.4))+0.6log_{2}(1/(0.6))

解

簡約

0.4 \cdot lo g_{2} (\frac{1}{0.4}) + 0.6 \cdot lo g_{2} (\frac{1}{0.6})

lo g_{2} (1.96013 \dots)

十進法表記

0.97095 \dots

解答ステップ

0.4 lo g_{2} (\frac{1}{0.4}) + 0.6 lo g_{2} (\frac{1}{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} (\frac{1}{0.4}) = lo g_{2} ((\frac{1}{0.4})^{0.4})

= lo g_{2} ((\frac{1}{0.4})^{0.4}) + 0.6 lo g_{2} (\frac{1}{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} (\frac{1}{0.6}) = lo g_{2} ((\frac{1}{0.6})^{0.6})

= lo g_{2} ((\frac{1}{0.4})^{0.4}) + lo g_{2} ((\frac{1}{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} ((\frac{1}{0.4})^{0.4}) + lo g_{2} ((\frac{1}{0.6})^{0.6}) = lo g_{2} ((\frac{1}{0.4})^{0.4} (\frac{1}{0.6})^{0.6})

= lo g_{2} ((\frac{1}{0.4})^{0.4} (\frac{1}{0.6})^{0.6})

(\frac{1}{0.4})^{0.4} (\frac{1}{0.6})^{0.6} = 1.96013 \dots

= lo g_{2} (1.96013 \dots)