# 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.