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受欢迎的代数 >

4^{2x}-5*4^{x+2}+1021=0

解答

4^{2 x} - 5 \cdot 4^{x + 2} + 1021 = 0

解答

x = \frac{ln ( 40 + 579 )}{2 ln ( 2 )}, x = \frac{ln ( 40 - 579 )}{2 ln ( 2 )}

+1

十进制

x = 3.00070 \dots, x = 1.99718 \dots

求解步骤

4^{2 x} - 5 \cdot 4^{x + 2} + 1021 = 0

使用指数运算法则

(4^{x})^{2} - 5 \cdot 4^{x} \cdot 4^{2} + 1021 = 0

用

4^{x} = u

改写方程式

(u)^{2} - 5 u \cdot 4^{2} + 1021 = 0

解

u^{2} - 5 u \cdot 4^{2} + 1021 = 0 : u = 40 + 579, u = 40 - 579

u = 40 + 579, u = 40 - 579

代回

u = 4^{x}

，求解

x

解

4^{x} = 40 + 579 : x = \frac{ln ( 40 + 579 )}{2 ln ( 2 )}

解

4^{x} = 40 - 579 : x = \frac{ln ( 40 - 579 )}{2 ln ( 2 )}

x = \frac{ln ( 40 + 579 )}{2 ln ( 2 )}, x = \frac{ln ( 40 - 579 )}{2 ln ( 2 )}

作图

流行的例子

5^{3x+2}-3*5^{6x+2}-100=0

5^{3 x + 2} - 3 \cdot 5^{6 x + 2} - 100 = 0

3*6^x=4.5(e^2)^x

3 \cdot 6^{x} = 4.5 (e^{2})^{x}

solvefor x,3^x=27

so l v e f or x, 3^{x} = 27

solvefor x,3^x=81

so l v e f or x, 3^{x} = 81

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