If $n$ is a natural number such that\n $n = p_{1}^{\alpha_{1}} \cdot p_{2}^{\alpha_{2}} \cdot p_{3}^{\alpha_{3}}\ldots\ldots p_{k}^{\alpha_{k}}$\n and $p_{1},p_{2},\ldots.p_{k}$ are distinct primes, then show that\n $logn \geq klog2$.