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受欢迎的代数 >

10^{2x}-5(10^x)+6=0

解答

1 0^{2 x} - 5 (1 0^{x}) + 6 = 0

解答

x = \frac{ln ( 3 )}{ln ( 10 )}, x = \frac{ln ( 2 )}{ln ( 10 )}

+1

十进制

x = 0.47712 \dots, x = 0.30102 \dots

求解步骤

1 0^{2 x} - 5 (1 0^{x}) + 6 = 0

使用指数运算法则

(1 0^{x})^{2} - 5 \cdot 1 0^{x} + 6 = 0

用

1 0^{x} = u

改写方程式

(u)^{2} - 5 u + 6 = 0

解

u^{2} - 5 u + 6 = 0 : u = 3, u = 2

u = 3, u = 2

代回

u = 1 0^{x}

，求解

x

解

1 0^{x} = 3 : x = \frac{ln ( 3 )}{ln ( 10 )}

解

1 0^{x} = 2 : x = \frac{ln ( 2 )}{ln ( 10 )}

x = \frac{ln ( 3 )}{ln ( 10 )}, x = \frac{ln ( 2 )}{ln ( 10 )}

作图

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