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受欢迎的代数 >

3^x+3^{2-x}=11

解答

3^{x} + 3^{2 - x} = 11

解答

x = \frac{ln ( \frac{11 + 85}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{11 - 85}{2} )}{ln ( 3 )}

+1

十进制

x = 2.10584 \dots, x = - 0.10584 \dots

求解步骤

3^{x} + 3^{2 - x} = 11

使用指数运算法则

3^{x} + (3^{x})^{- 1} \cdot 3^{2} = 11

用

3^{x} = u

改写方程式

u + (u)^{- 1} \cdot 3^{2} = 11

解

u + u^{- 1} \cdot 3^{2} = 11 : u = \frac{11 + 85}{2}, u = \frac{11 - 85}{2}

u = \frac{11 + 85}{2}, u = \frac{11 - 85}{2}

代回

u = 3^{x}

，求解

x

解

3^{x} = \frac{11 + 85}{2} : x = \frac{ln ( \frac{11 + 85}{2} )}{ln ( 3 )}

解

3^{x} = \frac{11 - 85}{2} : x = \frac{ln ( \frac{11 - 85}{2} )}{ln ( 3 )}

x = \frac{ln ( \frac{11 + 85}{2} )}{ln ( 3 )}, x = \frac{ln ( \frac{11 - 85}{2} )}{ln ( 3 )}

作图

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