When log is written without a base, is the equation normally referring to log base 10 or natural log?

For example, this question presents the equation

\omega(n) < \frac{\log n}{\log \log n} + 1.4573 \frac{\log n}{(\log \log n)^{2}},

but I'm not entirely sure if this is referring to log base 10 or the natural logarithm.

Answer

In mathematics, \log n is most often taken to be the natural logarithm. The notation \ln(x) not seen frequently past multivariable calculus, since the logarithm base 10 finds relatively little use.

This Wikipedia page gives a classification of where each definition, that is base 2, e and 10, are used:

\log (x) refers to \log_2 (x) in computer science and information theory.

\log(x) refers to \log_e(x) or the natural logrithm in mathematical analysis, physics, chemistry, statistics, economics, and some engineering fields.

\log(x) refers to \log_{10}(x) in various engineering fields, logarithm tables, and handheld calculators.

Attribution
Source : Link , Question Author : john smith , Answer Author : Community

Leave a Comment