Since the natural logarithm, i.e. with base $e$, is very commonly used in research papers and that both $\ln(x)$ and $\log(x)$ are used to denote it, it is natural* to ask which of these notations to use when preparing a paper. The fact that both are used in literature concerning the same topics gives rise to unnecessary confusions and/or definitions. Both have their advantages and disadvantages:
- The notation $\ln(x)$ bears no ambiguity, as its name is the abbreviation of the French logarithme naturel, or natural logarithm. One does not need to define what it denotes, it is self-explanatory. However, not everyone likes to use it, because...
- The notation $\log(x)$ is used much more widely for historical reasons as well as notational conventions. However, literally every time it is mentioned in a paper, it is followed by something along the lines of "where $\log(x)$ denotes the natural logarithm, whose base value is $e$", which is not only cumbersome for the reader (who has read this phrase a hundred times before), but can also be avoided by simply using $\ln(x)$.
So which notation is best suited for denoting $\log_e(x)$ and why?
*pun not intended