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 >

2x+3^x=13

解答

2 x + 3^{x} = 13

解答

x = - \frac{2 W _{0} ( \frac{e ^{\frac{13 l n ( 3 )}{2}} l n ( 3 )}{2} ) - 13 ln ( 3 )}{2 ln ( 3 )}

+1

十进制

x = 2

求解步骤

2 x + 3^{x} = 13

将

2 x + 3^{x} = 13

调整为朗伯形式:

1 = (13 - 2 x) e^{- l n (3) x}

用

(- x + \frac{13}{2}) ln (3) = u

和

x = - \frac{2 u - 13 ln ( 3 )}{2 ln ( 3 )}

改写方程式

1 = (13 - 2 (- \frac{2 u - 13 ln ( 3 )}{2 ln ( 3 )})) e^{- l n (3) (- \frac{2 u - 13 l n ( 3 )}{2 l n ( 3 )})}

化简

1 = e^{\frac{2 u - 13 l n ( 3 )}{2}} (13 + \frac{2 u - 13 ln ( 3 )}{ln ( 3 )})

改写

1 = e^{\frac{2 u - 13 l n ( 3 )}{2}} (13 + \frac{2 u - 13 ln ( 3 )}{ln ( 3 )})

为朗伯形式:

e^{u} u = \frac{e ^{\frac{13 l n ( 3 )}{2}} ln ( 3 )}{2}

解

e^{u} u = \frac{e ^{\frac{13 l n ( 3 )}{2}} ln ( 3 )}{2} : u = W_{0} (\frac{e ^{\frac{13 l n ( 3 )}{2}} ln ( 3 )}{2})

u = W_{0} (\frac{e ^{\frac{13 l n ( 3 )}{2}} ln ( 3 )}{2})

代回

u = (- x + \frac{13}{2}) ln (3)

，求解

x

解

(- x + \frac{13}{2}) ln (3) = W_{0} (\frac{e ^{\frac{13 l n ( 3 )}{2}} ln ( 3 )}{2}) : x = - \frac{2 W _{0} ( \frac{e ^{\frac{13 l n ( 3 )}{2}} l n ( 3 )}{2} ) - 13 ln ( 3 )}{2 ln ( 3 )}

x = - \frac{2 W _{0} ( \frac{e ^{\frac{13 l n ( 3 )}{2}} l n ( 3 )}{2} ) - 13 ln ( 3 )}{2 ln ( 3 )}

作图

流行的例子

(9/7)^3*(49/81)^{2x-6}=(7/9)^9

(\frac{9}{7})^{3} \cdot (\frac{49}{81})^{2 x - 6} = (\frac{7}{9})^{9}

(x/(10))-20.89*e^{(-x)/((2478.82))}=0

(\frac{x}{10}) - 20.89 \cdot e^{\frac{- x}{( 2478.82 )}} = 0

solvefor x,p^2-p(e^x+e^{-x})+1=0

so l v e f or x, p^{2} - p (e^{x} + e^{- x}) + 1 = 0

2^{n - 1} = 16

14e^{6-x}+e^{12x-7}=0

14 e^{6 - x} + e^{12 x - 7} = 0