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

it is an abomination introduced by the manufacturers of pocket calculators", $\ln$ was used as early as 1893 in Irving Stringham's bookUniplanar Algebra(see p. 41). You can also find $\ln$ used in Charles Smith's 1900 bookElementary Algebra for the Use of Schools and Colleges(see p. 437). $\endgroup$ – Dave L Renfro Aug 21 '17 at 19:19