It is fair to say that historically log has referred to base 10 logarithms whereas ln has referred to base e logarithms called the natural logarithm. However, some mathematicians have of late suggested that we use log for all logarithms and use the base e as the normal base. Notably, that is the position of Leonard Gillman. In fact, I was present at one meeting where he advocated that and I watched the heated discussion that followed. I must say that his arguments convinced me that he is right. In fact, if you see the calculus text by Gillman & McDowell that is the convention in that book.