I'm guessing you wanted to write $\displaystyle \log(n!)=O(n\log n)$, and this follows from $\displaystyle \log(n!)=\sum\limits_{k=1}^n\log n\le n\log n$ ...
In mathematics, (log2 n) is called the binary logarithm (the logarithm for base 2).It can be written like lg n.The binary logarithm is often used in computer science.Hence, maybe u didn't see this notation.