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受欢迎的代数 >

-(ln(1-x))/x =1.5

解答

- \frac{ln ( 1 - x )}{x} = 1.5

解答

x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{3}

+1

十进制

x = 0.58281 \dots

求解步骤

- \frac{ln ( 1 - x )}{x} = 1.5

在两边乘以

x

- ln (1 - x) = 1.5 x

在两边乘以

10

- ln (1 - x) \cdot 10 = 15 x

两边除以

- 10

ln (1 - x) = - \frac{3 x}{2}

若

f (x) = g (x)

，则

a^{f (x)} = a^{g (x)}

e^{l n (1 - x)} = e^{- \frac{3 x}{2}}

化简

e^{l n (1 - x)} : 1 - x

1 - x = e^{- \frac{3 x}{2}}

解

1 - x = e^{- \frac{3 x}{2}} : x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{3}, x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{3}

x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{3}, x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{3}

验证解:

x = \frac{2 W _{- 1} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{3}

假

, x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{3}

真

解是

x = \frac{2 W _{0} ( - \frac{3}{2 e ^{\frac{3}{2}}} ) + 3}{3}

作图

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