# Log-likelihood of the normal distribution.

On the attached picture I've highlighted the term which I do not agree with. Is it actually true ? In my calculations I get $$-n(\frac{1}{2}\log(\sqrt{2\pi})+\log(\sigma)),$$ instead. Thank you in advance.

• Notice that $0.5 \log(\sigma^2)=\log(\sigma)$. So $\sigma$ terms coincide. $\log \pi$ is often omitted because this is a constant not affecting anything. But formally speaking you are correct.Nevertheless log-likelihood is often claimed to be defined up to constant addend. – Alexander Vigodner Sep 12 '14 at 15:44