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.
|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|
|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.