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?




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\*pun not intended



$\log(x)$ or $\ln(x)$ to denote the natural logarithm in research papers?
In number theory, the notation $ \log $ is commonly used, especially when asymptotics are considered. One also frequently uses the notation $ \log\_{k} $ for the $ k $ -th iterate of this function. Indeed the natural logarithm is essentially the only one that matters. This may not be true for other subfields of mathematics.


