Log log ln

1. Apr 8, 2006

sweetvirgogirl

my complex analysis book uses all three of them...

although i know the difference between log and ln, I'm kinda clueless about Log ... any ideas?

2. Apr 8, 2006

devious_

It's probably the principle value of log. I'm sure your book has it mentioned somewhere.

3. Apr 8, 2006

4. Apr 9, 2006

TD

In my textbook, log was used to denote the 'old' logarithm for real values only, and Log for the complex logarithm (i.e. Log(z) = log(r) + i*phi, with phi the phase, if I recall correctly).

5. Apr 10, 2006

sweetvirgogirl

let me tell you how my textbook defines certain terms ...

log z = ln |z| + i * arg z
Log z = ln |z| + i * Arg z

now consider this example:
log (1+ i * 3^(1/2)
now the value I would get is ... ln |1+ i * 3 ^(1/2)| + i ( pi/3 + 2 n pi)
which simplifies to ln 2 + i (pi/3 +2 n pi)

now the answer in the back of the book is log 2 + i (pi/3 +2 n pi)
and this is not the first time they have done it ... so i dont think it's a typo ...

lol ... mind explaning how they replaced ln 2 with log 2??
thanks!

6. Apr 10, 2006

sweetvirgogirl

another thing ...
why do they always use n2pi (n = 0, , 1, -1, 2, -2...)??
coz the values in case of tangent give the same value for n * pi

7. Apr 10, 2006

sweetvirgogirl

hmmm... bump?

8. Apr 10, 2006

shmoe

Your task is to now look up how they define arg and Arg. Most likely, Arg will denote some 'principle branch' and be a single valued function while arg is the multivalued version.

In advanced textbooks (=beyond intro calculus) "log" usually denotes the base e logarithm, i.e. the "ln" on your calculator. They probably explain this somewhere in your text.