Logarithm Notation

[mmm4444bot]

I came across the following notation in a calculus book:

a^x and ln_a​x are inverses

This is the first time that I have seen a base-subscript written on ln.

Is ln used to denote logarithms involving bases other than Euler's Number?

 

[Deleted member 4993]

I came across the following notation in a calculus book:



This is the first time that I have seen a base-subscript written on ln.

Is ln used to denote logarithms involving bases other than Euler's Number?

Wherever I had encountered ln, it was abbreviation of log natural.

This - I suppose - falls in the catagory of "you know what I mean ....."

But then it is written in english - isn't it? ( reference to Mark's signature line...)

 

[srmichael]

I came across the following notation in a calculus book:



This is the first time that I have seen a base-subscript written on ln.

Is ln used to denote logarithms involving bases other than Euler's Number?

First time I've ever seen that. By definition ln means base e. [i.e. Log_ex = ln(x)]. Not sure what the author had in mind. Did it expand on that notation in some way or did it simply state that little diddy? Perhaps it was a typo and he meant a^x and log_ax are inverses.

 

[lookagain]

I came across the following notation in a calculus book:



This is the first time that I have seen a base-subscript written on ln.

It is wrong.

 

[pka]

It is wrong.

I don't think it is fair to call any mathematical notation wrong if the author defines it.
Look at this page.
The history of logarithms is filled with many different notations for the logarithm.
I have actually been present for a argument between two department heads about whether to use a particular calculus textbook because it used \(\displaystyle \log(x)\) in place of \(\displaystyle \ln(x)\).

Frankly I have seen \(\displaystyle \ln_b(x)\) as well as \(\displaystyle \text{lg}_b(x)\) used.

 

[mmm4444bot]

Did [the book] expand on that notation in some way or did it simply state that little diddy?

The notation simply appears, out of the blue. I've just started reading the book (a somewhat comical presentation of introductory calculus topics). I don't expect any explanation, but I'll be watching for clues, as I continue reading.

The quoted example was in a list of three examples of inverse relationships. I understand the example (log functions are inverses of power functions, vice versa), but the notation struck me; I'm not sure why ln was chosen to represent logs in general -- by adding the subscript.

There are always new things for me to learn. This situation of novelty reminds me of the time that I learned, on these boards, that zero can be either a positive number or a negative number. I had never heard of that one, before, either; but those interpretations of zero apparently have precedence.)

PKA and Subhotosh make good points. Notations evolve, and we often need to take some stuff for granted.

I won't argue against writing ln_a -- but I won't use it, either. :cool:

 

[lookagain]

I will always use the ISO Standard given for the natural logarithm as seen below: Example	Meaning and verbal equivalent	Remarks
e	base of natural logarithms	e = 2.718 28...
ex	exponential function to the base e of x
logax	logarithm to the base a of x
lb x	binary logarithm (to the base 2) of x	lb x = log2x
ln x	natural logarithm (to the base e) of x	ln x = logex
lg x	common logarithm (to the base 10) of x	lg x = log10x
...	...	...

Source:

http://en.wikipedia.org/wiki/ISO_31-11

 

[mmm4444bot]

I will always use the ISO Standard given for the natural logarithm​

Makes sense to me!

 

[HallsofIvy]

Thanks lookagain.

I do not think anyone even mentioned binary logs back when I was in school. (Just checked. My book on mathematical tables (1959 edition) has various log and antilog tables starting on page 18 and running through page 92 and then again from 136 through 139, but nothing about binary logs.)

Ah, but you and I went to school in years "B.C."!

(Before Computers!)