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受欢迎的代数 >

2^{(-x)}+2^x=5

解答

2^{(- x)} + 2^{x} = 5

解答

x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 2 )}, x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 2 )}

+1

十进制

x = 2.26041 \dots, x = - 2.26041 \dots

求解步骤

2^{(- x)} + 2^{x} = 5

使用指数运算法则

(2^{x})^{- 1} + 2^{x} = 5

用

2^{x} = u

改写方程式

(u)^{- 1} + u = 5

解

u^{- 1} + u = 5 : u = \frac{5 + 21}{2}, u = \frac{5 - 21}{2}

u = \frac{5 + 21}{2}, u = \frac{5 - 21}{2}

代回

u = 2^{x}

，求解

x

解

2^{x} = \frac{5 + 21}{2} : x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 2 )}

解

2^{x} = \frac{5 - 21}{2} : x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 2 )}

x = \frac{ln ( \frac{5 + 21}{2} )}{ln ( 2 )}, x = \frac{ln ( \frac{5 - 21}{2} )}{ln ( 2 )}

作图

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