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受欢迎的代数 >

m^{sqrt(m)}= 1/2

解答

m^{m} = \frac{1}{2}

解答

m = \frac{1}{16}, m = \frac{1}{4}

+1

十进制

m = 0.0625, m = 0.25

求解步骤

m^{m} = \frac{1}{2}

将

m^{m} = \frac{1}{2}

调整为朗伯形式:

m e^{\frac{l n ( 2 )}{m}} = 1

用

- \frac{ln ( 2 )}{m} = u

和

m = \frac{ln ^{2} ( 2 )}{u ^{2}}

改写方程式

(\frac{ln ^{2} ( 2 )}{u ^{2}}) e^{- u} = 1

解

(\frac{ln ^{2} ( 2 )}{u ^{2}}) e^{- u} = 1 : u = - 4 ln (2), u = - 2 ln (2), u = 2 W_{0} (\frac{ln ( 2 )}{2})

u = - 4 ln (2), u = - 2 ln (2), u = 2 W_{0} (\frac{ln ( 2 )}{2})

代回

u = - \frac{ln ( 2 )}{m}

，求解

m

解

- \frac{ln ( 2 )}{m} = - 4 ln (2) : m = \frac{1}{16}

解

- \frac{ln ( 2 )}{m} = - 2 ln (2) : m = \frac{1}{4}

解

- \frac{ln ( 2 )}{m} = 2 W_{0} (\frac{ln ( 2 )}{2}) : m \in R

无解

m = \frac{1}{16}, m = \frac{1}{4}

验证解:

m = \frac{1}{16}

真

, m = \frac{1}{4}

真

解为

m = \frac{1}{16}, m = \frac{1}{4}

验证解:

m = \frac{1}{16}

真

, m = \frac{1}{4}

真

解为

m = \frac{1}{16}, m = \frac{1}{4}

作图

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10 = 58 \cdot e^{- 90 k} + 2

x ln (e^{x}) + x = 12

x^{10} = 2^{x}

8^{5x-7}=9^{2x-3}

8^{5 x - 7} = 9^{2 x - 3}