As taught in China, we use the $log$ to represent the most general logarithm which needs a base and an antilogarithm clarified, for example, $\log_39$. When the base is 10, we use the symbol $lg$, and when the base is $e$ we use $ln$. For those that take 2 as the base, we also use a distinctive symbol $lb$, so that everything is clear without ambiguity.
But after I started my postgraduate study in Japan I noticed that different countries actually have different habits on this when they use a plain $log$ without designating the base. And it also differs from field to field. For instance, in signal processing, especially for sound signal, $log$ is used as $lg$ to describe the magnitude of a spectrum; in information theory, $log$ is used as $lb$ when calculating the information entropy; and in mathematics when doing the maximum likelihood estimation or handling with complex numbers, $log$ again stands for $ln$.
That is with no doubt confusing, especially in research papers, when different authors have different usage habits of the $log$. But I think what we can do is to try to understand what they really refer to through the context and avoid using that plain $log$ ourselves.