x^lgx=x^3/100的解集?答案为10与100.

x^lgx=x^3/100的解集?
答案为10与100.

由原方程,显然x>0
两边取对数得
(logx)^2=3logx-2
(logx)^2-3logx+2=0
(logx+1)(logx+2)=0
=> logx=-1 或 logx=-2
=> x=1/10 或 x=1/100
x∈{1/10,1/100}