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受欢迎的代数 >

化简-(3/14)log_{2}(3/14)-(2/14)log_{2}(2/14)

解答

化简

- (\frac{3}{14}) lo g_{2} (\frac{3}{14}) - (\frac{2}{14}) lo g_{2} (\frac{2}{14})

解答

\frac{lo g _{2} ( \frac{16807}{27} ) + 3}{14}

+1

十进制

0.87727 \dots

求解步骤

- (\frac{3}{14}) lo g_{2} (\frac{3}{14}) - (\frac{2}{14}) lo g_{2} (\frac{2}{14})

- (\frac{3}{14}) lo g_{2} (\frac{3}{14}) - (\frac{2}{14}) lo g_{2} (\frac{2}{14}) = - \frac{3}{14} lo g_{2} (\frac{3}{14}) + \frac{1}{7} lo g_{2} (7)

= - \frac{3}{14} lo g_{2} (\frac{3}{14}) + \frac{1}{7} lo g_{2} (7)

- \frac{3}{14} lo g_{2} (\frac{3}{14}) = - lo g_{2} ((\frac{3}{14})^{\frac{3}{14}})

\frac{1}{7} lo g_{2} (7) = lo g_{2} (7^{\frac{1}{7}})

= - lo g_{2} ((\frac{3}{14})^{\frac{3}{14}}) + lo g_{2} (7^{\frac{1}{7}})

使用对数计算法则:

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

lo g_{2} (7^{\frac{1}{7}}) - lo g_{2} ((\frac{3}{14})^{\frac{3}{14}}) = lo g_{2} \frac{7 ^{\frac{1}{7}}}{( \frac{3}{14} ) ^{\frac{3}{14}}}

= lo g_{2} \frac{7 ^{\frac{1}{7}}}{( \frac{3}{14} ) ^{\frac{3}{14}}}

(\frac{3}{14})^{\frac{3}{14}} = 14 \frac{27}{2744}

= lo g_{2} \frac{7 ^{\frac{1}{7}}}{14 \frac{27}{2744}}

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 ^{\frac{1}{7}}}{14 \frac{27}{2744}} = lo g_{2} (7^{\frac{1}{7}}) - lo g_{2} (14 \frac{27}{2744})

= lo g_{2} (7^{\frac{1}{7}}) - lo g_{2} (14 \frac{27}{2744})

lo g_{2} (7^{\frac{1}{7}}) = \frac{1}{7} lo g_{2} (7)

= \frac{1}{7} lo g_{2} (7) - lo g_{2} (14 \frac{27}{2744})

\frac{1}{7} lo g_{2} (7) - lo g_{2} (14 \frac{27}{2744}) = \frac{1}{7} lo g_{2} (7) - \frac{1}{14} lo g_{2} (\frac{27}{2744})

= \frac{1}{7} lo g_{2} (7) - \frac{1}{14} lo g_{2} (\frac{27}{2744})

\frac{1}{7} lo g_{2} (7) - \frac{1}{14} lo g_{2} (\frac{27}{2744}) = \frac{- \frac{1}{2} lo g _{2} ( \frac{27}{2744} ) + lo g _{2} ( 7 )}{7}

= \frac{- \frac{1}{2} lo g _{2} ( \frac{27}{2744} ) + lo g _{2} ( 7 )}{7}

- \frac{1}{2} lo g_{2} (\frac{27}{2744}) + lo g_{2} (7) = \frac{- 3 lo g _{2} ( 3 ) + 3 + 5 lo g _{2} ( 7 )}{2}

= \frac{\frac{- 3 l o g _{2} ( 3 ) + 3 + 5 l o g _{2} ( 7 )}{2}}{7}

使用分式法则:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{- 3 lo g _{2} ( 3 ) + 3 + 5 lo g _{2} ( 7 )}{2 \cdot 7}

数字相乘:

2 \cdot 7 = 14

= \frac{- 3 lo g _{2} ( 3 ) + 3 + 5 lo g _{2} ( 7 )}{14}

- 3 lo g_{2} (3) + 3 + 5 lo g_{2} (7) = lo g_{2} (\frac{16807}{27}) + 3

= \frac{lo g _{2} ( \frac{16807}{27} ) + 3}{14}

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