CMO 1989 Problem 6

Find all functions $f:(1,+\infty) \rightarrow (1,+\infty)$ that satisfy the following condition: for arbitrary $x,y>1$ and $u,v>0$ , inequality $f(x^uy^v)\le f(x)^{\dfrac{1}{4u}}f(y)^{\dfrac{1}{4v}}$ holds.