thank you very much!! now I think I conquer this kind of problems!
I can find the solution of another similar question by myself (cheers!!)
Quesion is y=logx and y=cx^4 have only one intersection, what is the value of c?
The answer is 1/4e.
let f(x)=logx-cx^4=0 which means f(x) has only one intersction with x-axis.
x>square1/4c, f'(x)<0 f(x) go decrease
x<square1/4c, f'(x)>0, f(x) go increase
so f(x=square1/4c) must be 0 so that f(x) has only one intersection with x-axis.