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受欢迎的代数 >

3^{x+1}=3^{2x-1}+6

解答

3^{x + 1} = 3^{2 x - 1} + 6

解答

x = \frac{ln ( 6 )}{ln ( 3 )}, x = 1

+1

十进制

x = 1.63092 \dots, x = 1

求解步骤

3^{x + 1} = 3^{2 x - 1} + 6

使用指数运算法则

3^{x} \cdot 3^{1} = (3^{x})^{2} \cdot 3^{- 1} + 6

用

3^{x} = u

改写方程式

u \cdot 3^{1} = (u)^{2} \cdot 3^{- 1} + 6

解

u \cdot 3^{1} = u^{2} \cdot 3^{- 1} + 6 : u = 6, u = 3

u = 6, u = 3

代回

u = 3^{x}

，求解

x

解

3^{x} = 6 : x = \frac{ln ( 6 )}{ln ( 3 )}

解

3^{x} = 3 : x = 1

x = \frac{ln ( 6 )}{ln ( 3 )}, x = 1

作图

流行的例子

5^{4 - x} = 0

7^{x} = 2 \cdot 5^{x}

6^{x} = \frac{1}{6}

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

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

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