Log is a logarithm with any arbitrary base, for example log_10 100=2.
Ln is a logarithm with a base of e(Euler's number), which is 2.71828 18284 59045 23536...
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To enter a natural log, press the LN button. To enter a log with base 10, press the LOG button. To enter a log with a base other than those, divide the log of the number with the log of the base, so log6(8) would be log(8)/log(6) or ln(8)/ln(6). (The ln is preferred because in calculus it is easier to work with.)
in most cases they are the same
You divide log 8 / log 16. Calculate the logarithm in any base, but use the same base for both - for example, ln 8 / ln 16.
in math, ln means natural log, or loge and e means 2.718281828
ln is the natural logarithm. That is it is defined as log base e. As we all know from school, log base 10 of 10 = 1 just as log base 3 of 3 = 1, so, likewise, log base e of e = 1 and 1.x = x. so we have ln y = x. Relace ln with log base e, and you should get y = ex