方程3/(3^x-1)+1/3=3^(x-1)的实数解

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/15 23:55:00
方程3/(3^x-1)+1/3=3^(x-1)的实数解方程3/(3^x-1)+1/3=3^(x-1)的实数解方程3/(3^x-1)+1/3=3^(x-1)的实数解令y=3^x,y>0原方程即3/(y-

方程3/(3^x-1)+1/3=3^(x-1)的实数解
方程3/(3^x-1)+1/3=3^(x-1)的实数解

方程3/(3^x-1)+1/3=3^(x-1)的实数解
令 y = 3^x,y>0
原方程即
3/(y-1) + 1/3 = y/3
同乘以 3(y-1)
9 + y-1 = y(y-1)
y^2 - 2y - 8 = 0
(y+2)(y-4)=0
y=-2(舍去),y=4
∴ 3^x = 4
x = log3 (4)
(以3为底4的对数)

x= log3 4