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受欢迎的代数 >

e^{-x}(1+x)=0.005

解答

e^{- x} (1 + x) = 0.005

解答

x = - W_{- 1} (- \frac{0.005}{e}) - 1, x = - W_{0} (- \frac{0.005}{e}) - 1

+1

十进制

x = 7.43012 \dots, x = - 0.99815 \dots

求解步骤

e^{- x} (1 + x) = 0.005

用

- x - 1 = u

和

x = - u - 1

改写方程式

e^{- (- u - 1)} (1 + (- u - 1)) = 0.005

化简

- e^{u + 1} u = 0.005

改写

- e^{u + 1} u = 0.005

为朗伯形式:

e^{u} u = - \frac{0.005}{e}

解

e^{u} u = - \frac{0.005}{e} : u = W_{- 1} (- \frac{0.005}{e}), u = W_{0} (- \frac{0.005}{e})

u = W_{- 1} (- \frac{0.005}{e}), u = W_{0} (- \frac{0.005}{e})

代回

u = - x - 1

，求解

x

解

- x - 1 = W_{- 1} (- \frac{0.005}{e}) : x = - W_{- 1} (- \frac{0.005}{e}) - 1

解

- x - 1 = W_{0} (- \frac{0.005}{e}) : x = - W_{0} (- \frac{0.005}{e}) - 1

x = - W_{- 1} (- \frac{0.005}{e}) - 1, x = - W_{0} (- \frac{0.005}{e}) - 1

作图

流行的例子

e^{2 t} - 3 e^{t} = 0

5 = 2 5^{x}

32 = 2^{p}

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7^{log_{7}(x)+log_{7}(3)}=12

7^{l o g_{7} (x) + l o g_{7} (3)} = 12