order of growth of a counting function

Question

Let $\{a_n\}$ be a sequence of complex numbers. For every $t>0$, define $n(t)=$ the number of $a_n$ satisfying the inequality $|a_n|\leq t$. We call $n(r)$ the counting function for the sequence. In the book "Lectures on entire functions" by Levin, i read that the order of growth of $n(r)$ is $$\rho=\limsup_{r\rightarrow +\infty}\frac{log \ n(r)}{log \ r}$$ How can i understand/prove this formula?