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受欢迎的代数 >

(500)/(100-e^{x/2)}=20

解答

\frac{500}{100 - e ^{\frac{x}{2}}} = 20

解答

x = 2 ln (75)

+1

十进制

x = 8.63497 \dots

求解步骤

\frac{500}{100 - e ^{\frac{x}{2}}} = 20

在两边乘以

100 - e^{\frac{x}{2}}

\frac{500}{100 - e ^{\frac{x}{2}}} (100 - e^{\frac{x}{2}}) = 20 (100 - e^{\frac{x}{2}})

化简

500 = 20 (100 - e^{\frac{x}{2}})

交换两边

20 (100 - e^{\frac{x}{2}}) = 500

两边除以

20

100 - e^{\frac{x}{2}} = 25

将

100

到右边

- e^{\frac{x}{2}} = - 75

两边除以

- 1

e^{\frac{x}{2}} = 75

使用指数运算法则

\frac{x}{2} = ln (75)

解

\frac{x}{2} = ln (75) : x = 2 ln (75)

x = 2 ln (75)

验证解:

x = 2 ln (75)

真

解是

x = 2 ln (75)

作图

流行的例子

2^{x+1}+2^{x-2}= 9/2

2^{x + 1} + 2^{x - 2} = \frac{9}{2}

2^{x+3}-2^x=112

2^{x + 3} - 2^{x} = 112

x \times 2^{x - 1} = 32

3^{x+1}+3^x+3^{x+1}=39

3^{x + 1} + 3^{x} + 3^{x + 1} = 39

3^{\frac{x}{3}} = 99