Prove that $n=O(n\log n)$ using the definition

Question

The definition:
given two functions $f$ and $g$, $f(n)$ is in the class $O(g(n))$ if there exist constants $N$ and $c$ such that $f(n)<c ⋅ g(n)$ when $n > N$.

Answer 1

Hint:

When $N\ge3$, for all $n\ge N$, $\log n\ge\log N >1$, so $n < n \log n$ whenever $n > N$.