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 >

2^{2x+3}-57=65(2^x-1)

解答

2^{2 x + 3} - 57 = 65 (2^{x} - 1)

解答

x = 3, x = - 3

求解步骤

2^{2 x + 3} - 57 = 65 (2^{x} - 1)

使用指数运算法则

(2^{x})^{2} \cdot 2^{3} - 57 = 65 (2^{x} - 1)

用

2^{x} = u

改写方程式

(u)^{2} \cdot 2^{3} - 57 = 65 (u - 1)

解

u^{2} \cdot 2^{3} - 57 = 65 (u - 1) : u = 8, u = \frac{1}{8}

u = 8, u = \frac{1}{8}

代回

u = 2^{x}

，求解

x

解

2^{x} = 8 : x = 3

解

2^{x} = \frac{1}{8} : x = - 3

x = 3, x = - 3

作图

流行的例子

4^{2x}+4^{2x-1}=4

4^{2 x} + 4^{2 x - 1} = 4

3^{x-2}=9a^{x-4}

3^{x - 2} = 9 a^{x - 4}

solvefor x,2^{5x}+2^{8y}=2^{13z}

so l v e f or x, 2^{5 x} + 2^{8 y} = 2^{13 z}

solvefor n,x^n=0

so l v e f or n, x^{n} = 0

solvefor x,q(3^{2x+1})=54

so l v e f or x, q (3^{2 x + 1}) = 54