Senior Mathematical Challenge 2015 Q25

A function, defined on the set of positive integers, is such that $f\left(xy\right)=f\left(x\right)+f\left(y\right)$ for all $x$ and $y$. It is known that $f\left(10\right)=14$ and $f\left(40\right)=20$.

What is the value of $f\left(500\right)$?