the misadventures of weather boy: This was fun without a calculator:

Friday, February 11, 2005

This was fun without a calculator:

Problem: Find the integer n for which this is true.
8n log₂n < 4n²

The answer is 5, which is what I deduced (the two terms equal each other when n=2 and n=4), but it was extremely fun trying to figure out if I was right.

Unfortunately, I missed the related problem:
Find the given c and n for which 4n² is in Ω(8n log₂n). I set c=1, and I had thought the answer would be the same as above. Wrong! If c=1, n=4, since 4n² ≤ c*8n log₂n for Ω.

METAR KRDU 111651Z 31509KT 10SM FEW150 04/M14 A3003 RMK SLP174