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受欢迎的代数 >

(2^x+2^{-x})/2 =3

解答

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

解答

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

+1

十进制

x = 2.54310 \dots, x = - 2.54310 \dots

求解步骤

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

在两边乘以

2

\frac{2 ^{x} + 2 ^{- x}}{2} \cdot 2 = 3 \cdot 2

化简

2^{x} + 2^{- x} = 6

使用指数运算法则

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

用

2^{x} = u

改写方程式

u + (u)^{- 1} = 6

解

u + u^{- 1} = 6 : u = 3 + 22, u = 3 - 22

u = 3 + 22, u = 3 - 22

代回

u = 2^{x}

，求解

x

解

2^{x} = 3 + 22 : x = \frac{ln ( 3 + 2 2 )}{ln ( 2 )}

解

2^{x} = 3 - 22 : x = \frac{ln ( 3 - 2 2 )}{ln ( 2 )}

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

作图

流行的例子

solvefor y,3^x+5^y=x^3+y

so l v e f or y, 3^{x} + 5^{y} = x^{3} + y

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3^{2 x + 1} = 7^{x - 2}

2 e^{5 x + 2} = 17

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9^{x} = \frac{1}{3 3}

4x^2e^{-x^2}-2e^{-x^2}=0

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