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 >

4^x(5^2x)=10

解答

4^{x} (5^{2} x) = 10

解答

x = \frac{W _{0} ( \frac{4 l n ( 2 )}{5} )}{2 ln ( 2 )}

+1

十进制

x = 0.27370 \dots

求解步骤

4^{x} (5^{2} x) = 10

将

4^{x} (5^{2} x) = 10

调整为朗伯形式:

e^{2 l n (2) (x + 2 l o g_{4} (5))} x = 10

用

2 ln (2) x = u

和

x = \frac{u}{2 ln ( 2 )}

改写方程式

e^{2 l n (2) ((\frac{u}{2 l n ( 2 )}) + 2 l o g_{4} (5))} (\frac{u}{2 ln ( 2 )}) = 10

化简

\frac{e ^{u + 4 l n (2) l o g_{4} (5)} u}{2 ln ( 2 )} = 10

改写

\frac{e ^{u + 4 l n (2) l o g_{4} (5)} u}{2 ln ( 2 )} = 10

为朗伯形式:

e^{u} u = \frac{4 ln ( 2 )}{5}

解

e^{u} u = \frac{4 ln ( 2 )}{5} : u = W_{0} (\frac{4 ln ( 2 )}{5})

u = W_{0} (\frac{4 ln ( 2 )}{5})

代回

u = 2 ln (2) x

，求解

x

解

2 ln (2) x = W_{0} (\frac{4 ln ( 2 )}{5}) : x = \frac{W _{0} ( \frac{4 l n ( 2 )}{5} )}{2 ln ( 2 )}

x = \frac{W _{0} ( \frac{4 l n ( 2 )}{5} )}{2 ln ( 2 )}

作图

流行的例子

40000=5400*1.035^x

40000 = 5400 \cdot 1.03 5^{x}

e^{9 x} = 4

2^{3x}-2^{7x-2}=0

2^{3 x} - 2^{7 x - 2} = 0

-5*7^{-3x-6}-8=-9

- 5 \cdot 7^{- 3 x - 6} - 8 = - 9

4 = 3^{x - 3}