Inequality with the prime-counting function

Hi there guys, I hope I've posted this in the right section;

I'm going through a paper, and there is one statement which is:

$\displaystyle n^{\pi(n)} < 3^n $

for sufficiently large $\displaystyle n$, where $\displaystyle \pi(n)$ is the prime-counting function defined as the function counting the number of prime numbers less than or equal to $\displaystyle n$. I'm having real difficulty justifying this claim, and I'd be really grateful if someone could help me out.

Thanks in advance,

HTale