Find a positive real number $C$ and a nonnegative real number $x_o$ such that
$Cx$$\log x$ $\leq$ $\log x!$ for all real numbers $x > x_o$.
I tried to expand $\log x!$ into $\log 1 + \log2 +\log3 +....\log x$. But how do I choose $C$ and $x_o$ so the above inequality hold?
Any hints would be appreciated.