```So far as I have seen, almost any recently published, high-selling
textbook in calculus -- as distinct from advanced calculus or analysis
-- aimed at the U.S. market uses ln rather than log for the natural
logarithm.

No wonder students are confused when they go on to a more advanced
course and suddenly it's log, not ln.

Then of course there's the issue that computer scientists often use log
to mean base-2 log.

Andrzej Kozlowski wrote:
> Tthe notation ln seems to have become essentially extinct since the
> disappearance of slide rules. It fact, was almost never used in books
> on analysis or calculus aimed at mathematicians. I have just checked and
> Dieudonne, Foundations of Modern Analysis, published in 1969 uses log,
> Apostol, Calculus, published in 1967 uses log, Rudin, "Principles of
> Modern Analysis", published in 1964 uses L after remarking that "the
> usual notation is, of corse, log"), Rudin "Real and complex analysis",
> published in 1970 uses (naturally) log. Of 5 books that I have looked
> at only one, Fichtenholtz - A course of differential and integral
> calculus (in Russian) published in 1966 uses ln, which is presumably
> because it was aimed at engineers, who in those days still used slide
> rules (at least in Russia). (In spite of that, it is still a rather
> good book).
>
> Andrzej Kozlowski
>
>
> On 4 Feb 2009, at 11:18, Murray Eisenberg wrote:
>
>> No, in mathematics log x or log(x) is a perfectly acceptable, perhaps
>> the predominant, notation for the base-e, natural logarithm.
>>
>> In calculus books, ln x or ln(x) is typically used for that --  so as
>> not to confuse students who were taught that log means the base-10
>> logarithm.
>>
>> O.T.: P.S. M.I.T. has an all-male a cappella singing group named the
>> "Logarhythms".
>>
>> slawek wrote:
>>> The natural logarithm function in "traditional form" in Mathematica
>>> (version
>>> 6.0.2.0)
>>>
>>>  log(x)
>>>
>>> This is "not a bug but a feature", but in mathematics the natural
>>> logarithm
>>> is just ln(x) or even ln x.
>>> The true traditional notation use log for decimal logarithm, ln for
>>> natural
>>> logarithm, lb for binary logarithm, and
>>> log_{b}x  for logarithm with base b. Unfortunatelly in most computer
>>> programs (see FORTRAN) LOG
>>> stands for natural logarithm (an exception is Pascal).
>>>
>>> Nevertheless, how to force to use ln(x) instead log(x) ?
>>>
>>> The brute way is use /.Log->ln//TraditionalForm.
>>>
>>> Is any more elegant way to do this?
>>>
>>> slawek
>>>
>>>
>> --
>> Murray Eisenberg                     murray at math.umass.edu
>> Mathematics & Statistics Dept.
>> Lederle Graduate Research Tower      phone 413 549-1020 (H)
>> University of Massachusetts                413 545-2859 (W)
>> 710 North Pleasant Street            fax   413 545-1801
>> Amherst, MA 01003-9305
>>
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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