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受欢迎的代数 >

(1/4)^x+(1/2)^x-6=0

解答

(\frac{1}{4})^{x} + (\frac{1}{2})^{x} - 6 = 0

解答

x = - 1

求解步骤

(\frac{1}{4})^{x} + (\frac{1}{2})^{x} - 6 = 0

使用指数运算法则

((\frac{1}{2})^{x})^{2} + (\frac{1}{2})^{x} - 6 = 0

用

(\frac{1}{2})^{x} = u

改写方程式

(u)^{2} + u - 6 = 0

解

u^{2} + u - 6 = 0 : u = 2, u = - 3

u = 2, u = - 3

代回

u = (\frac{1}{2})^{x}

，求解

x

解

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

解

(\frac{1}{2})^{x} = - 3 : x \in R

无解

x = - 1

作图

流行的例子

8*3^{n-1}-21=51

8 \cdot 3^{n - 1} - 21 = 51

3^{2x}-10× 3^x+21=0

3^{2 x} - 10 \times 3^{x} + 21 = 0

9 \cdot 2^{2 x} = 1

\sqrt[3]{(2^7-2^x)/(2^x-2)}=2

3 \frac{2 ^{7} - 2 ^{x}}{2 ^{x} - 2} = 2

solvefor x,2^x=16

so l v e f or x, 2^{x} = 16