I know this is a ridiculous question, but what is the domain of ln (x) ?
Is it > 0 ???
ln(x) is the inverse function of e^y.
So the domain of ln(x) is the range of e^y. So yes, the domain of ln(x) is x>0, because for no y do we have e^y<0 or e^y=0, but for every x>0, there is a y such that e^y=x.
The natural log of a number x is the power to which e would be raised to equal x. Note that e is positive, and you can't raise a positive number to any power and get a negative number, so what numbers for x can you plug into ln(x) for it to make sense? Also note that when speaking of domain and range, it is best to say explicitly what set of numbers they belong to (in this case the positive reals).
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