Exploring Logarithms: What You Need to Know

  • Thread starter sweetvirgogirl
  • Start date
  • Tags
    Logarithms
In summary: 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.
  • #1
sweetvirgogirl
116
0
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?
 
Physics news on Phys.org
  • #2
It's probably the principle value of log. I'm sure your book has it mentioned somewhere.
 
  • #4
sweetvirgogirl said:
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?
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
TD said:
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).
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 don't think it's a typo ...

lol ... mind explaning how they replaced ln 2 with log 2??
thanks!
 
  • #6
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
hmmm... bump?
 
  • #8
sweetvirgogirl said:
log z = ln |z| + i * arg z
Log z = ln |z| + i * Arg z

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.

sweetvirgogirl said:
... mind explaning how they replaced ln 2 with log 2??

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.
 

1. What are logarithms?

Logarithms are mathematical functions that represent the inverse of exponential functions. They are used to solve equations involving exponential expressions and to compare large numbers.

2. Why are logarithms important?

Logarithms are important because they allow us to simplify complex calculations involving large numbers. They also have many applications in fields such as science, engineering, and finance.

3. How do you solve logarithmic equations?

To solve logarithmic equations, you can use properties of logarithms such as the product rule, quotient rule, and power rule. You can also use the definition of a logarithm and algebraic manipulation to solve equations.

4. What is the relationship between logarithms and exponents?

Logarithms and exponents are inverse functions of each other. This means that if a number is raised to a certain power, the logarithm of that number is the exponent. For example, if 2^3 = 8, then log2 8 = 3.

5. How are logarithms used in real life?

Logarithms are used in a variety of real-life applications, such as earthquake magnitude scales, pH scales, and measuring the loudness of sounds. They are also used in finance to calculate compound interest and in science to model exponential growth and decay.

Similar threads

Replies
5
Views
1K
Replies
4
Views
685
Replies
2
Views
1K
Replies
1
Views
741
  • Calculus
Replies
3
Views
1K
Replies
10
Views
909
Replies
8
Views
2K
  • Calculus
Replies
7
Views
2K
Replies
2
Views
1K
Back
Top