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受欢迎的代数 >

4^{x+1}+2^{x-2}=68

解答

4^{x + 1} + 2^{x - 2} = 68

解答

x = \frac{ln ( \frac{- 1 + 17409}{32} )}{ln ( 2 )}

+1

十进制

x = 2.03279 \dots

求解步骤

4^{x + 1} + 2^{x - 2} = 68

使用指数运算法则

(2^{x})^{2} \cdot 2^{2} + 2^{x} \cdot 2^{- 2} = 68

用

2^{x} = u

改写方程式

(u)^{2} \cdot 2^{2} + u \cdot 2^{- 2} = 68

解

u^{2} \cdot 2^{2} + u \cdot 2^{- 2} = 68 : u = \frac{- 1 + 17409}{32}, u = \frac{- 1 - 17409}{32}

u = \frac{- 1 + 17409}{32}, u = \frac{- 1 - 17409}{32}

代回

u = 2^{x}

，求解

x

解

2^{x} = \frac{- 1 + 17409}{32} : x = \frac{ln ( \frac{- 1 + 17409}{32} )}{ln ( 2 )}

解

2^{x} = \frac{- 1 - 17409}{32} : x \in R

无解

x = \frac{ln ( \frac{- 1 + 17409}{32} )}{ln ( 2 )}

作图

流行的例子

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

5^{x} = 5^{2 x + 1}

5^{x^2}=(1/25)^{x+3}

5^{x^{2}} = (\frac{1}{25})^{x + 3}

(2^x)/(3^{x+1)}=1

\frac{2 ^{x}}{3 ^{x + 1}} = 1

4^{(2x-1)}= 1/2

4^{(2 x - 1)} = \frac{1}{2}