# Appropriate graphic symbol for log()?

• Twinbee
In summary, the symbol ^ is commonly used for exponentiation in the computer world, but there is no universal symbol for logarithms. The usual notation is "ln" for natural log and "log" for base 10, with other bases written in subscript. However, a new operator is suggested that unifies all types of logarithms into one symbol. Possible choices for this symbol include a unicode character such as ˅ or ᵛ, or an arrow down.
Twinbee
In the computer world at least, the symbol ^ is often used for exponentiation.

I was just wondering if log has had anything in the multitude of languages out there. It would be nice to see an operator such as "1000¬10=3" instead of writing LogBase10(1000)=3 which is more ugly. I'm writing a calculator, so I'd include the new symbol in that.

If such a symbol hasn't been already used, I'd be grateful for suggestions, especially ones which are already on US/UK keyboards (maybe one of these: ¬ ` ¦ | \ @ ~ )

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The usual notation is "ln" for natural log and "log" for base 10. Other bases are usually written using a subscript.

Yes I realize that, but the arbitrary-base log function is kind of the opposite of the power operator. You wouldn't necessarily want numbers 10 or e as the default base when using exponentiation. If people were forced to forego the general x^y and instead only allowed to use pow(4) or exp(4) to mean 10^4 or e^4 respectively, there'd be lots of complaints.

Likewise, instead of only having ln, log and logbase, with all the initial confusion and kludgy notation all that provides, why not just (also) have a single operator which unifies them all as described in my first post?

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The latex code for a superscript is ^. The latex code for a subscript is _. It would seem to me that this is the closest thing to a character representing subscript. The problem is that underscore is used much more generally in programming. There is also the problem that no character by itself really lends itself to the same type of notation.

3^4 works well because there is only one character needed, between the exponent and base.
log_3 81 isn't as nice. Here the word log serves as the operator, and the underscore only serves to designate the base.

I suppose you could do a similar thing as exponents and use only a single character between the numbers. I don't really like this though as it is too ambiguous.

3_81 is wrong because 81 isn't a subscript.
81_3 is wrong because it is in the wrong order.

It's probably no coincidence that there is no real convention for logs.

Thanks, I overlooked the underscore!

Since we're creating a new operator so to speak, previous notation rules for log() can be suspended for now. Therefore, I'm not sure which order is better:

10_100 =2 (closer to old notation)
100_10 =2 (perhaps more consistent generally, feels like divide almost)

An arrow down would be nice for the symbol (the user would press underscore, but the editor would come up with an arrow). Potential unicode characters include:

U+02C5 ˅ Modifier Letter Down Arrowhead
U+1D5B ᵛ Modifier Letter Small V
U+2227 ∨ Logical OR (don't want to use this, as I need OR in the calc)

My only reservation is that any of the above look pretty close to a logical OR, apart from being smaller. Of course, ¬ is also taken (logical not), so maybe I should choose a different unicode symbol (I'll keep underscore for what the user actually presses though - nice one).

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## 1. What is a graphic symbol for log()?

The most commonly used graphic symbol for log() is the letter "log" with a subscript "b" to represent the base of the logarithm. Another common symbol is "ln" for the natural logarithm.

## 2. Why is a graphic symbol needed for log()?

A graphic symbol is needed for log() to represent the mathematical function visually. It makes it easier for readers to understand and recognize the function in equations or graphs.

## 3. How is the graphic symbol for log() different from other mathematical functions?

The graphic symbol for log() is unique in that it includes a subscript to represent the base of the logarithm. Other mathematical functions may have different symbols and do not typically include a subscript.

## 4. Are there other variations of the graphic symbol for log()?

Yes, there are some variations of the graphic symbol for log() that may be used in different contexts. For example, some may use "lg" instead of "log" to represent the base-10 logarithm.

## 5. Can the graphic symbol for log() be changed or customized?

Yes, the graphic symbol for log() can be changed or customized in certain situations, such as in programming languages or in specialized fields of study. However, it is important to use a well-recognized symbol to avoid confusion and inconsistencies.

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