Solving logaritm equation

[MattiasMath]

I've run into a dead end trying to solve this equation and I was hoping that someone here might be able to point me in the right direction!

1. The problem statement, all variables and given/known data
xlgx = x4/1000


2. Relevant equations
-


3. The attempt at a solution
xlgx = x4/1000
lg(xlgx) = lg(x4/1000)
(lgx)2 = lg(x4) - lg(1000)
(lgx)2 = 4lgx - 3

Now after this point I'm not sure what to do. I tried:
3 = 4lgx - (lgx)2
3 = lgx * (4 - lgx)

But that doesn't seem to lead me anywhere. Any help would be much appreciated!

[issacnewton]

you have a quadratic equation in \log(x)

let t=\log(x) and solve quadratic equation in t

[MattiasMath]

Of course, obviously!

Thanks a lot for your help, much appreciated.