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受欢迎的代数 >

3^{x-1}+3^{4-x}=36

解答

3^{x - 1} + 3^{4 - x} = 36

解答

x = \frac{ln ( 9 ( 6 + 33 ) )}{ln ( 3 )}, x = \frac{ln ( 9 ( 6 - 33 ) )}{ln ( 3 )}

+1

十进制

x = 4.24227 \dots, x = 0.75772 \dots

求解步骤

3^{x - 1} + 3^{4 - x} = 36

使用指数运算法则

3^{x} \cdot 3^{- 1} + (3^{x})^{- 1} \cdot 3^{4} = 36

用

3^{x} = u

改写方程式

u \cdot 3^{- 1} + (u)^{- 1} \cdot 3^{4} = 36

解

u \cdot 3^{- 1} + u^{- 1} \cdot 3^{4} = 36 : u = 9 (6 + 33), u = 9 (6 - 33)

u = 9 (6 + 33), u = 9 (6 - 33)

代回

u = 3^{x}

，求解

x

解

3^{x} = 9 (6 + 33) : x = \frac{ln ( 9 ( 6 + 33 ) )}{ln ( 3 )}

解

3^{x} = 9 (6 - 33) : x = \frac{ln ( 9 ( 6 - 33 ) )}{ln ( 3 )}

x = \frac{ln ( 9 ( 6 + 33 ) )}{ln ( 3 )}, x = \frac{ln ( 9 ( 6 - 33 ) )}{ln ( 3 )}

作图

流行的例子

ln (e^{x} - 3) = 2

5^{2 x} = 20

4 - 3^{x} = 0

16^{2x+1}=9^{3x-4}

1 6^{2 x + 1} = 9^{3 x - 4}

16^{2x-3}4^{-2x}=16

1 6^{2 x - 3} 4^{- 2 x} = 16