Log n Grows Slowly

The function log(n) grows so slowly that it can almost be considered to be the same as 1.

A good rule: log₂(1000) ≈ 10, since 2¹⁰ = 1024.

         10 bits ≈ 3 decimal digits.         

	n	log2(n)
students in CS 314	240	8
students at UT	50,000	16
people in US	300,000,000	28
people on earth	7,000,000,000	33
national debt	19,500,000,000,000	45
Library of Congress, bytes	20*1012	45
earth surface area, mm2	5*1020	69
atoms in universe	1080	266

Thus, we can say that log₂(n) < 300 for any problem that we are likely to see. If we simply wrote 300 instead of log₂(n), our rule tells us to eliminate the constant 300.