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+10^x=25^x

解答

4^{x} + 1 0^{x} = 2 5^{x}

解答

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{5}{2} )}

+1

十进制

x = 0.52517 \dots

求解步骤

4^{x} + 1 0^{x} = 2 5^{x}

两边除以

4^{x}

\frac{4 ^{x}}{4 ^{x}} + \frac{1 0 ^{x}}{4 ^{x}} = \frac{2 5 ^{x}}{4 ^{x}}

化简

1 + (\frac{5}{2})^{x} = (\frac{25}{4})^{x}

使用指数运算法则

1 + (\frac{5}{2})^{x} = ((\frac{5}{2})^{x})^{2}

用

(\frac{5}{2})^{x} = u

改写方程式

1 + u = (u)^{2}

解

1 + u = u^{2} : u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

u = \frac{1 + 5}{2}, u = \frac{1 - 5}{2}

代回

u = (\frac{5}{2})^{x}

，求解

x

解

(\frac{5}{2})^{x} = \frac{1 + 5}{2} : x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{5}{2} )}

解

(\frac{5}{2})^{x} = \frac{1 - 5}{2} : x \in R

无解

x = \frac{ln ( \frac{1 + 5}{2} )}{ln ( \frac{5}{2} )}

作图

流行的例子

1/(2^x)+1/(2^x)+1/(2^x)=3

\frac{1}{2 ^{x}} + \frac{1}{2 ^{x}} + \frac{1}{2 ^{x}} = 3

(2^x)^6=(2^9)^2

(2^{x})^{6} = (2^{9})^{2}

4^{x-1}*(0.5)^{3-2x}=(1/8)^x

4^{x - 1} \cdot (0.5)^{3 - 2 x} = (\frac{1}{8})^{x}

3^{1-x}= 1/((sqrt(3)))

3^{1 - x} = \frac{1}{( 3 )}

4 \cdot 3^{x} = 324