Bhavya,

How far can you throw that textbook? Go give it a try and then come back when you're finished for the answer. No, don't: first find out at what power of n less than 1 they do think the transition happens, tell me, then go see how far you can chuck it. I'm curious <grin>

In fact, for any a<1<b, and any k>0, we have

n^a < n/(lg(n)^k) < n < n (lg(n)^k) < n^b

and in particular n^0.99 < n/lg(n).

You are quite right that these matters are hard to check on a calculator. The logarithm grows exceedingly slowly!

Good Hunting!
RD