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受欢迎的代数 >

5^{x+1}+5^{1-x}=11

解答

5^{x + 1} + 5^{1 - x} = 11

解答

x = \frac{ln ( \frac{11 + 21}{10} )}{ln ( 5 )}, x = \frac{ln ( \frac{11 - 21}{10} )}{ln ( 5 )}

+1

十进制

x = 0.27560 \dots, x = - 0.27560 \dots

求解步骤

5^{x + 1} + 5^{1 - x} = 11

使用指数运算法则

5^{x} \cdot 5^{1} + (5^{x})^{- 1} \cdot 5^{1} = 11

用

5^{x} = u

改写方程式

u \cdot 5^{1} + (u)^{- 1} \cdot 5^{1} = 11

解

u \cdot 5^{1} + u^{- 1} \cdot 5^{1} = 11 : u = \frac{11 + 21}{10}, u = \frac{11 - 21}{10}

u = \frac{11 + 21}{10}, u = \frac{11 - 21}{10}

代回

u = 5^{x}

，求解

x

解

5^{x} = \frac{11 + 21}{10} : x = \frac{ln ( \frac{11 + 21}{10} )}{ln ( 5 )}

解

5^{x} = \frac{11 - 21}{10} : x = \frac{ln ( \frac{11 - 21}{10} )}{ln ( 5 )}

x = \frac{ln ( \frac{11 + 21}{10} )}{ln ( 5 )}, x = \frac{ln ( \frac{11 - 21}{10} )}{ln ( 5 )}

作图

流行的例子

-7*3^{0.25x}=-10

- 7 \cdot 3^{0.25 x} = - 10

2^{-x}*2^{3x}=64

2^{- x} \cdot 2^{3 x} = 64

9^{3p}=27^{1-3p}

9^{3 p} = 2 7^{1 - 3 p}

e^{x - 1} - 2 = 0

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

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