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