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?
The ‘e’ base is an interesting choice in calculus. For example, the derivative of ln(x) wrt x is 1/x. The derivative of log10(x) wrt x is 1/(ln(10)x). The natural logarithm automatically pops up!
on top of that, ‘e’ is the only base b such that d/dx b^x = b^x. every other base induces some multiplicative factor in the derivative, hence why it’s considered the ‘natural’ base for exponentials and logarithms.