optimization - How to simplify the summation of log

I have a summation that involve log. I don't know how to solve this summation. I want to find an expression (even a good approximation is enough) for this summation.

$\sum_{k=0}^{n}{log(a_k)}$

or
$log(\prod_{k=0}^{n}{a_k})$

I only know that
$\sum_{k=0}^{n}{a_k}= N$

Any help Please?

Edit

Let $a_k$ is a random variable which can take its value according to binomial (or normal) distribution. Then how to solve the above log summation problem.