化简-(5/8)log_{2}(5/8)-(3/8)log_{2}(3/8)

解答

化简

- (\frac{5}{8}) lo g_{2} (\frac{5}{8}) - (\frac{3}{8}) lo g_{2} (\frac{3}{8})

- lo g_{2} (884375) + 3

十进制

0.95443 \dots

求解步骤

- (\frac{5}{8}) lo g_{2} (\frac{5}{8}) - (\frac{3}{8}) lo g_{2} (\frac{3}{8})

使用法则:

(a) = a

(\frac{5}{8}) = \frac{5}{8}

= - \frac{5}{8} lo g_{2} (\frac{5}{8}) - \frac{3}{8} lo g_{2} (\frac{3}{8})

- \frac{5}{8} lo g_{2} (\frac{5}{8}) = - lo g_{2} ((\frac{5}{8})^{\frac{5}{8}})

- \frac{3}{8} lo g_{2} (\frac{3}{8}) = - lo g_{2} ((\frac{3}{8})^{\frac{3}{8}})

= - lo g_{2} ((\frac{5}{8})^{\frac{5}{8}}) - lo g_{2} ((\frac{3}{8})^{\frac{3}{8}})

使用对数计算法则:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

- lo g_{2} ((\frac{3}{8})^{\frac{3}{8}}) - lo g_{2} ((\frac{5}{8})^{\frac{5}{8}}) = lo g_{2} ((\frac{3}{8})^{\frac{3}{8}} (\frac{5}{8})^{\frac{5}{8}})

= - lo g_{2} ((\frac{3}{8})^{\frac{3}{8}} (\frac{5}{8})^{\frac{5}{8}})

化简

(\frac{3}{8})^{\frac{3}{8}} (\frac{5}{8})^{\frac{5}{8}} : \frac{8 84375}{8}

= - lo g_{2} (\frac{8 84375}{8})

使用对数计算法则:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{2} (\frac{8 84375}{8}) = lo g_{2} (884375) - lo g_{2} (8)

= - (lo g_{2} (884375) - lo g_{2} (8))

lo g_{2} (8) = 3

= - (lo g_{2} (884375) - 3)

使用分配律:

- (a - b) = - a + b

- (lo g_{2} (884375) - 3) = - lo g_{2} (884375) + 3

= - lo g_{2} (884375) + 3

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