What's the definition of log, ln, lg, lb
Bernhard Seebass
as ln(x) is the inverse to e^x. But than I came across the following
definitions:
ln(x) : inverse function to e^x
lg(x) : " " " 10^x
lb(x) : " " " 2^x
log(x) : not defined unless the base is explicitly declared, e.g.
log7(x). (7 should be subscript)
Well, I have to admit, the book where I found this, wasn't the very
latest one and probably those definitions were copied from some even
more ancient book etc.
Now, my questions: Is there some acknowledged definition (IUPAC /
ANSI ..) which is to be applied? Are there different customs in
different countries? (my book is a German one)
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Mark Chrisman
Bernhard Seebass <bsee...@org.chem.ethz.ch> writes:
> Until yesterday, I thought log(x) were the inverse function of 10^x
> as ln(x) is the inverse to e^x. But than I came across the following
> definitions:
> ln(x) : inverse function to e^x
> lg(x) : " " " 10^x
> lb(x) : " " " 2^x
> log(x) : not defined unless the base is explicitly declared, e.g.
> log7(x). (7 should be subscript)
>
> Well, I have to admit, the book where I found this, wasn't the very
> latest one and probably those definitions were copied from some even
> more ancient book etc.
> Now, my questions: Is there some acknowledged definition (IUPAC /
> ANSI ..) which is to be applied? Are there different customs in
> different countries? (my book is a German one)
I wouldn't be suprised if these were notations the author introduced solely
for his book.
"ln" always means base e. I've never seen "lb" or "lg" before (which may
simply mean I haven't read the right books).
The meaning of "log" varies, depending on the subject. In elementary
calculus texts, it always (in my experience) means base 10. In more advanced
analysis texts, it means base e (and base 10 logs are never used). In
computer science books, it often means base 2. (In many applications - for
example, time complexity of an algorithm - the base doesn't matter, since
logs to different bases differ by constants.) I don't know about engineering
or physics books -- probably base 10.
--------------------------------------------------------
Mark Chrisman (if your reply is of general interest
please post it, don't email it. Thanks!)
"An earlier version of myself proved this theorem, but
I'll have to take his word for it, since I'm too tired
to think about it right now."
Dave Seaman
Bernhard Seebass <bsee...@org.chem.ethz.ch> wrote:
>Until yesterday, I thought log(x) were the inverse function of 10^x
>as ln(x) is the inverse to e^x. But than I came across the following
>definitions:
>ln(x) : inverse function to e^x
>lg(x) : " " " 10^x
>lb(x) : " " " 2^x
>log(x) : not defined unless the base is explicitly declared, e.g.
>log7(x). (7 should be subscript)
It's been my experience that "log" means "whichever type of log I use most."
In other words,
"log" = "log_e" to pure mathematicians,
"log" = "log_10" to applied mathematicians and and in natural science,
"log" = "log_2" to computer scientists.
I have also seen "lg" used to mean "log_2" in computer science, and
"ln" tends to get used for "log_e" mostly in calculus classes, but not
so much in higher-level math. "Of course 'log' means 'log natural': that's
why it's called 'natural.'"
The rest of it looks pretty nonstandard to me, but any author is free
to set the conventions in his own textbook or paper.
--
Dave Seaman
Randall C. Poe
|> In article <3d45iq$k...@elna.ethz.ch>
|> Bernhard Seebass <bsee...@org.chem.ethz.ch> writes:
|>
|> > Now, my questions: Is there some acknowledged definition (IUPAC /
|> I don't know about engineering
|> or physics books -- probably base 10.
|>
In physics, log(x) is usually taken to mean the log base e, since it arises
in so many places. Log_10 is an artifact of our numbering system.
God help us if we let IUPAC or ANSI standardize mathematical notation...
Dmitrii Manin
o ln(x) : inverse function to e^x
o lg(x) : " " " 10^x
o lb(x) : " " " 2^x
o log(x) : not defined unless the base is explicitly declared, e.g.
o log7(x). (7 should be subscript)
o
o [....] Are there different customs in different countries? (my book
o is a German one)
The same notation is used in Russian-language literature (except lb,
which I have never seen, but can easily imagine). Customs do differ.
--
- M
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