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

用

2^{x} = u

改写方程式

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

解

u + u^{- 1} = 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

流行的例子

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5^{n} \cdot (\frac{1}{5})^{3} = 125

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4^{l o g_{2} (2 x)} = 36

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