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 >

(5^x)^2+8=125^2x

解答

(5^{x})^{2} + 8 = 12 5^{2} x

解答

x = - \frac{15625 W _{- 1} ( - \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} l n ( 5 )}{15625} ) - 16 ln ( 5 )}{31250 ln ( 5 )}, x = - \frac{15625 W _{0} ( - \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} l n ( 5 )}{15625} ) - 16 ln ( 5 )}{31250 ln ( 5 )}

+1

十进制

x = 3.37813 \dots, x = 0.00057 \dots

求解步骤

(5^{x})^{2} + 8 = 12 5^{2} x

将

(5^{x})^{2} + 8 = 12 5^{2} x

调整为朗伯形式:

1 = (15625 x - 8) e^{- 2 l n (5) x}

用

2 ln (5) (- x + \frac{8}{15625}) = u

和

x = - \frac{15625 u - 16 ln ( 5 )}{31250 ln ( 5 )}

改写方程式

1 = (15625 (- \frac{15625 u - 16 ln ( 5 )}{31250 ln ( 5 )}) - 8) e^{- 2 l n (5) (- \frac{15625 u - 16 l n ( 5 )}{31250 l n ( 5 )})}

化简

1 = e^{\frac{15625 u - 16 l n ( 5 )}{15625}} (- \frac{15625 u - 16 ln ( 5 )}{2 ln ( 5 )} - 8)

改写

1 = e^{\frac{15625 u - 16 l n ( 5 )}{15625}} (- \frac{15625 u - 16 ln ( 5 )}{2 ln ( 5 )} - 8)

为朗伯形式:

e^{u} u = - \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} ln ( 5 )}{15625}

解

e^{u} u = - \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} ln ( 5 )}{15625} : u = W_{- 1} (- \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} ln ( 5 )}{15625}), u = W_{0} (- \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} ln ( 5 )}{15625})

u = W_{- 1} (- \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} ln ( 5 )}{15625}), u = W_{0} (- \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} ln ( 5 )}{15625})

代回

u = 2 ln (5) (- x + \frac{8}{15625})

，求解

x

解

2 ln (5) (- x + \frac{8}{15625}) = W_{- 1} (- \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} ln ( 5 )}{15625}) : x = - \frac{15625 W _{- 1} ( - \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} l n ( 5 )}{15625} ) - 16 ln ( 5 )}{31250 ln ( 5 )}

解

2 ln (5) (- x + \frac{8}{15625}) = W_{0} (- \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} ln ( 5 )}{15625}) : x = - \frac{15625 W _{0} ( - \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} l n ( 5 )}{15625} ) - 16 ln ( 5 )}{31250 ln ( 5 )}

x = - \frac{15625 W _{- 1} ( - \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} l n ( 5 )}{15625} ) - 16 ln ( 5 )}{31250 ln ( 5 )}, x = - \frac{15625 W _{0} ( - \frac{2 e ^{\frac{16 l n ( 5 )}{15625}} l n ( 5 )}{15625} ) - 16 ln ( 5 )}{31250 ln ( 5 )}

作图

流行的例子

15 - 0. 5^{x} = - 6

solvefor a,m^{a+1}= 1/2

so l v e f or a, m^{a + 1} = \frac{1}{2}

64 = 2^{x}

2 = (1.1)^{x}

solvefor x,y^{12}=y^{2x}

so l v e f or x, y^{12} = y^{2 x}