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Name: Jake K.
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Question:
I would like to know: Why is the natural log labeled "ln" and not "nl".



Replies:
I am not sure there is a solid reason, but both "ln" (base e) and "log" (base 10) derive from the word "logarithm" hence the first letter is "L". The "n" may be derived from the name "Napier" who was the first to introduce "natural logs", but I am not sure. More likely it is an accident of history: "We have to name it something it distinguish it from base 10.

Recall that the definition of "Log(a)[X]" is the power (exponent) to which the number (a) (called the base) is raised so as to equal "X". So any number, excluding 0 and 1 can be used as the base. For example: Log2(16) = 4 (i.e. 2^4 = 16), and you can check that Log[pi](36.46216...) = pi. That is: (pi)^pi = 36.46216...



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