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2007-08-22 03:52:37 · 5 answers · asked by BlueEyedGrl 2 in Science & Mathematics Mathematics

5 answers

ln(-e) is a complex number (-e < 0)
ln(-e) = a+ib

log (ln) in the complex plane has multiple values.

e^(a+ib) = -e
e^a * e^(ib) = -e
e^a * (cosb + i.sinb) = -e
sin b = 0
b = 0 or pi
cos b = -1
b = pi
e^a * (-1) = -e
a = 1

ln(-e) = 1 + i(pi + 2pi.k) for all integral values of k

By convention, the notation should really be log(-e) to be precise.

2007-08-22 04:02:08 · answer #1 · answered by gudspeling 7 · 1 0

There is no logarithm of negative number
ln -e does not exist

2007-08-22 03:57:54 · answer #2 · answered by maussy 7 · 0 0

ln(-e) is undefined in real domain. The real domain of log(x) at any base is x>0.

2007-08-22 04:01:24 · answer #3 · answered by sahsjing 7 · 0 0

It is undefined.

Let ln(-e) = x.
Then, e^x = -e, which has no solution.

2007-08-22 04:01:44 · answer #4 · answered by Mr Placid 7 · 1 0

Think this only works with positive numbers.............. or else it takes a group.

2007-08-22 04:10:51 · answer #5 · answered by muddypuppyuk 5 · 0 0

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