
Glossary: Prime Pages: Top 5000: 
The function log x has two different standard
meanings. In most high school and lower division
college courses, log x is the common logarithm:
the power to which ten must be raised to get x.
In this sense, log 100 = 2.
However, in most upper division college courses, mathematical publications, and these pages, log x is the natural logarithm: the power to which e = 2.7182818284 5904523536 0287471352 6624977572 4709369995 9574966967 6277240766 3035354759 4571382178 5251664274 2746639193 2003059921 8174135966 2904357290 ...must be raised to get x. (This is sometimes denoted ln x in lower level texts and on most calculators.) So here log 100 = 4.60517... and log_{10} x = (log x)/(log 10). Why this is the "natural" base to use when dealing with prime numbers? The Prime Number Theorem states
Related pages (outside of this work) Chris K. Caldwell © 19992015 (all rights reserved)
