Question

ln (-2)

Answer 1

Is e, which is the base, a positive or a negative number?

Answer 2

this does not exist...logarithms can NOT have negative argument

Answer 3

@lgbasallote Sometimes it is best to lead the student to these conclusions.

Answer 4

\[\ln(-2)=\ln(e^{i \pi}*2)=\ln(2)+\ln(e^{i \pi})=\ln(2)+i \pi\]

Answer 5

logarithms can definitely have negative arguments :)

Answer 6

sorry...guess it's best to just say "logarithms cannot have negative arguments"? @Mertsj

Answer 7

hmmm i will bet dollars to donuts that when someone writes \(\ln(x)\) they are referring to the real valued function, whose domain is \(x>0\)

Answer 8

if it is the complex valued function, the usual notation is either \(\log\) or more commonly (if taking the principle branch) \(Log\)

Answer 9

and so if i was answering this question for my elementary functions or pre-calc course i would say "does not exist"

Answer 10

would it make sense if I did this, ln(-2) = e^ln-2 =-2