zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

250=((e^{42r}-1))/r

解答

250 = \frac{( e ^{42 r} - 1 )}{r}

解答

r = - \frac{125 W _{- 1} ( - \frac{21}{125 e ^{\frac{21}{125}}} ) + 21}{5250}

+1

十进制

r = 0.06921 \dots

求解步骤

250 = \frac{( e ^{42 r} - 1 )}{r}

将

250 = \frac{( e ^{42 r} - 1 )}{r}

调整为朗伯形式:

1 = (250 r + 1) e^{- 42 r}

用

- 42 r - \frac{21}{125} = u

和

r = - \frac{125 u + 21}{5250}

改写方程式

1 = (250 (- \frac{125 u + 21}{5250}) + 1) e^{- 42 (- \frac{125 u + 21}{5250})}

化简

1 = e^{\frac{125 u + 21}{125}} (- \frac{125 u + 21}{21} + 1)

改写

1 = e^{\frac{125 u + 21}{125}} (- \frac{125 u + 21}{21} + 1)

为朗伯形式:

e^{u} u = - \frac{21}{125 e ^{\frac{21}{125}}}

解

e^{u} u = - \frac{21}{125 e ^{\frac{21}{125}}} : u = W_{- 1} (- \frac{21}{125 e ^{\frac{21}{125}}}), u = W_{0} (- \frac{21}{125 e ^{\frac{21}{125}}})

u = W_{- 1} (- \frac{21}{125 e ^{\frac{21}{125}}}), u = W_{0} (- \frac{21}{125 e ^{\frac{21}{125}}})

代回

u = - 42 r - \frac{21}{125}

，求解

r

解

- 42 r - \frac{21}{125} = W_{- 1} (- \frac{21}{125 e ^{\frac{21}{125}}}) : r = - \frac{125 W _{- 1} ( - \frac{21}{125 e ^{\frac{21}{125}}} ) + 21}{5250}

解

- 42 r - \frac{21}{125} = W_{0} (- \frac{21}{125 e ^{\frac{21}{125}}}) : r = - \frac{125 W _{0} ( - \frac{21}{125 e ^{\frac{21}{125}}} ) + 21}{5250}

r = - \frac{125 W _{- 1} ( - \frac{21}{125 e ^{\frac{21}{125}}} ) + 21}{5250}, r = - \frac{125 W _{0} ( - \frac{21}{125 e ^{\frac{21}{125}}} ) + 21}{5250}

验证解:

r = - \frac{125 W _{- 1} ( - \frac{21}{125 e ^{\frac{21}{125}}} ) + 21}{5250}

真

, r = - \frac{125 W _{0} ( - \frac{21}{125 e ^{\frac{21}{125}}} ) + 21}{5250}

假

解是

r = - \frac{125 W _{- 1} ( - \frac{21}{125 e ^{\frac{21}{125}}} ) + 21}{5250}

验证解:

r = - \frac{125 W _{- 1} ( - \frac{21}{125 e ^{\frac{21}{125}}} ) + 21}{5250}

真

解是

r = - \frac{125 W _{- 1} ( - \frac{21}{125 e ^{\frac{21}{125}}} ) + 21}{5250}

作图

流行的例子

(5^{2})^{x} = 125

9^{x^2}*3^{7x}=81

9^{x^{2}} \cdot 3^{7 x} = 81

4^{x} + 2^{x} - 2 = 0

21 6^{x} = 26

9^{8 x - 7} = 1