[tex]\underbrace{\frac{n}{2}\times \frac{n}{2} \times \cdots \times \frac{n}{2}}_{\frac{n}{2}}\leq \underbrace{(\frac{n}{2} 1)\times (\frac{n}{2} 2) \times \cdots \times (\frac{n}{2} n)}_{\frac{n}{2}}\leq 1 \times 2 \times 3 \times \cdots \times n \Rightarrow {(\frac{n}{2})}^{\frac{n}{2}} \leq n! \Rightarrow \lg {(\frac{n}{2})}^{\frac{n}{2}} \leq \lg n![/tex]