I understand that log2 is useful for informatics, e.g. to determine how many bits I need to represent a given number. I understand that log10 is useful to determine the order of magnitude of numbers.
However, I’m having trouble understanding what makes ln interesting. It seems like it’s used a lot, but to me it just looks like a logarithm with a very weird base. What are the uses for this logarithm?
Your explanation makes a lot of sense to me! I didn’t know that
exp'(x) = exp(x), but can see how this could be an interesting property and in turn makeslninteresting.You saying, that it often doesn’t matter which logarithm is used, made me check and realize that
log_a(x)/log_a(y)is the same aslog_b(x)/log_b(y). Thus I understand that it really doesn’t make a difference which logarithm is used when “comparing the magnitude” (not sure if this is the right term) of numbers.I feel like I have a much better understanding of
lnnow. I’ll assume that the base of an algorithm is often basically a random choice and baseeis often used because of its “interesting trivia”.Thanks a lot!