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受欢迎的代数 >

化简-0.3log_{2}(0.3)-0.7log_{2}(0.7)

解答

化简

- 0.3 \cdot lo g_{2} (0.3) - 0.7 \cdot lo g_{2} (0.7)

解答

- lo g_{2} (\frac{7 ^{0.7} \cdot 3 ^{0.3}}{5}) + 1

+1

十进制

0.88129 \dots

求解步骤

- 0.3 lo g_{2} (0.3) - 0.7 lo g_{2} (0.7)

- 0.3 lo g_{2} (0.3) = - 0.3 lo g_{2} (\frac{3}{10})

0.7 = \frac{7}{10}

= - 0.3 lo g_{2} (\frac{3}{10}) - 0.7 lo g_{2} (\frac{7}{10})

- 0.3 lo g_{2} (\frac{3}{10}) = - lo g_{2} ((\frac{3}{10})^{0.3})

- 0.7 lo g_{2} (\frac{7}{10}) = - lo g_{2} ((\frac{7}{10})^{0.7})

= - lo g_{2} ((\frac{3}{10})^{0.3}) - lo g_{2} ((\frac{7}{10})^{0.7})

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{7}{10})^{0.7}) - lo g_{2} ((\frac{3}{10})^{0.3}) = lo g_{2} ((\frac{7}{10})^{0.7} (\frac{3}{10})^{0.3})

= - lo g_{2} ((\frac{7}{10})^{0.7} (\frac{3}{10})^{0.3})

化简

(\frac{7}{10})^{0.7} (\frac{3}{10})^{0.3} : \frac{7 ^{0.7} \cdot 3 ^{0.3}}{10}

= - lo g_{2} (\frac{7 ^{0.7} \cdot 3 ^{0.3}}{10})

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{7 ^{0.7} \cdot 3 ^{0.3}}{10}) = lo g_{2} (7^{0.7} \cdot 3^{0.3}) - lo g_{2} (10)

= - (lo g_{2} (7^{0.7} \cdot 3^{0.3}) - lo g_{2} (10))

lo g_{2} (7^{0.7} \cdot 3^{0.3}) = 0.7 lo g_{2} (7) + 0.3 lo g_{2} (3)

= - ((0.7 lo g_{2} (7) + 0.3 lo g_{2} (3)) - lo g_{2} (10))

使用法则:

(a) = a

(0.7 lo g_{2} (7) + 0.3 lo g_{2} (3)) = 0.7 lo g_{2} (7) + 0.3 lo g_{2} (3)

= - (0.7 lo g_{2} (7) + 0.3 lo g_{2} (3) - lo g_{2} (10))

lo g_{2} (10) = 1 + lo g_{2} (5)

= - (0.7 lo g_{2} (7) + 0.3 lo g_{2} (3) - (1 + lo g_{2} (5)))

使用分配律:

- (a + b) = - a - b

- (1 + lo g_{2} (5)) = - 1 - lo g_{2} (5)

= - (0.7 lo g_{2} (7) + 0.3 lo g_{2} (3) - 1 - lo g_{2} (5))

0.7 lo g_{2} (7) = lo g_{2} (7^{0.7})

0.3 lo g_{2} (3) = lo g_{2} (3^{0.3})

= - (lo g_{2} (7^{0.7}) + lo g_{2} (3^{0.3}) - 1 - lo g_{2} (5))

lo g_{2} (7^{0.7}) + lo g_{2} (3^{0.3}) - lo g_{2} (5) = lo g_{2} (\frac{7 ^{0.7} \cdot 3 ^{0.3}}{5})

= - (lo g_{2} (\frac{7 ^{0.7} \cdot 3 ^{0.3}}{5}) - 1)

使用分配律:

- (a - b) = - a + b

- (lo g_{2} (\frac{7 ^{0.7} \cdot 3 ^{0.3}}{5}) - 1) = - lo g_{2} (\frac{7 ^{0.7} \cdot 3 ^{0.3}}{5}) + 1

= - lo g_{2} (\frac{7 ^{0.7} \cdot 3 ^{0.3}}{5}) + 1

流行的例子

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s im pl i f y 14.77 + 10 lo g_{10} (\frac{179.68}{1.905})

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s im pl i f y 4 lo g_{10} (g) - 2 lo g_{10} (h)