why $\log(n!)$ isn't zero? I have wondered that why the  $\log (n!)$ isn't zero for $n \in N$.
Because I think that $\log (1)$ is zero so all following numbers after multiplying the result will become zero. 
Thanks in advance.

Might as well make an answer of it.
$$\begin{align*}
\lg(n!)&=\lg(1\cdot2\cdot3\cdot\ldots\cdot n)\\
&=\lg 1+\lg 2+\lg 3+\ldots+\lg n\\
&=\lg 2+\lg 3+\ldots+\lg n\;,
\end{align*}$$
so it won’t be $0$ unless $n=1$ (or $n=0$): you’re adding the logs, not multiplying them.
