58th Ukrainian National Mathematical Olympiad

Determine if there exist a function $f:(0;1)\to (2018;+\infty )$, so that the following conditions hold: $f(x\cdot y)=f(x)\cdot f(y)$ for any $x,y\in (0;1)$; for any $y\in (2018;+\infty )$ there exists $x\in (0;1)$ such that $f(x)=y$?