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受欢迎的代数 >

3^{2x}-6*3^{x+1}-243=0

解答

3^{2 x} - 6 \cdot 3^{x + 1} - 243 = 0

解答

x = 3

求解步骤

3^{2 x} - 6 \cdot 3^{x + 1} - 243 = 0

使用指数运算法则

(3^{x})^{2} - 6 \cdot 3^{x} \cdot 3^{1} - 243 = 0

用

3^{x} = u

改写方程式

(u)^{2} - 6 u \cdot 3^{1} - 243 = 0

解

u^{2} - 6 u \cdot 3^{1} - 243 = 0 : u = 27, u = - 9

u = 27, u = - 9

代回

u = 3^{x}

，求解

x

解

3^{x} = 27 : x = 3

解

3^{x} = - 9 : x \in R

无解

x = 3

作图

流行的例子

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