Perhaps am the only one wondering that...
Why the notation of the natural logarithm changes according to the reference is used. So, is the following TRUE? $$\ln{\left| x \right|} = \ln{x} = \log{x}$$
I always thought that $\log{x}$ was the notation convention to write the logarithm function with base $10$. So why can we write the previous equation!?
(comment from 3 weeks ago, with an additional paragraph, given as an answer, as requested by @Jesse P Francis. I'll add more later if I find that I have anything more to say that might be of interest.)
I think it's because the widespread use of the $\ln$ notation is relatively recent (50 or 60 years?) and mostly restricted to "school mathematics", which forms only a few years in the life of a practicing mathematics user. Personally, I always use $\ln$ when I intend natural logarithm because then there will be no possible ambiguity, but if you look through advanced undergraduate and graduate level complex variables textbooks, you'll find $\log$ used almost universally for natural logarithms.
In most papers and books before the 1880s (roughly speaking), logarithms were indicated by a lowercase "L" letter (and maybe sometimes an uppercase "L"), which I've personally found sometimes difficult to parse when digits are involved, especially the digit $1.$ For example, if you spend much time looking at older literature on infinite series (as I found myself doing several months ago for a project that I expect to eventually post in the History of Science and Math Stackexchange for an answer to an old question), you will see this "lowercase L notation" all over the place.