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受欢迎的代数 >

solvefor x,3^{2x}+2*3^{x+1}=16

解答

求解

x, 3^{2 x} + 2 \cdot 3^{x + 1} = 16

解答

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

+1

十进制

x = 0.63092 \dots

求解步骤

3^{2 x} + 2 \cdot 3^{x + 1} = 16

使用指数运算法则

(3^{x})^{2} + 2 \cdot 3^{x} \cdot 3^{1} = 16

用

3^{x} = u

改写方程式

(u)^{2} + 2 u \cdot 3^{1} = 16

解

u^{2} + 2 u \cdot 3^{1} = 16 : u = 2, u = - 8

u = 2, u = - 8

代回

u = 3^{x}

，求解

x

解

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

解

3^{x} = - 8 : x \in R

无解

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

作图

流行的例子

5^{2x-3}=3^{3x+4}

5^{2 x - 3} = 3^{3 x + 4}

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

4^{x^2+2}-9*2^{x^2+2}+8=0

4^{x^{2} + 2} - 9 \cdot 2^{x^{2} + 2} + 8 = 0

3^{x} + x = 30

(100)/(1+15e^{-0.4x)}=20

\frac{100}{1 + 15 e ^{- 0.4 x}} = 20