If we have a symbol for addition, subtraction, multiplication,

This video may interest you

https://www.youtube.com/watch?v=sULa9Lc4pck

the symbol for logarithm is "log", op

>>8815452
Thats pretty cool.

I also have a question about exponents.

If a^i is defined, is a^^i also defined(imagining ^ as arrow notation here)?

>>8815452
12 seconds in makes me want to go on a crusade to change conventional math notation.

The altered summation notation still doesn't feel perfect though.

>>8815447
We do have a symbol for logarithm. It's "log". Unlike the other operators, the symbol precedes both of its operands.

You do know that symbols can contain letters, right? Your question seems to have a false assumption embedded inside of it, like for example: "why doesn't the cosine function have a symbol?" -- a question which falsely assumes two things: (1) that the cosine function doesn't have a symbol, and (2) that "cos" is not a symbol.

>>8815472
>is a^^i also defined

https://en.wikipedia.org/wiki/Graham%27s_number

>>8815528
Do you know what [math]i[/math] is?

Because logarithm depends on the base, unlike addition and its buddies.

>>8815647
What makes log so special that it deserves to work differently from all the other operations which are just two numbers separated by a symbol?

>>8815452
His videos are some of the best recent content, but I don't like this one that much. It's too 3-dimensional and seems like it would be awkward to use in practice.

>>8815668
If you were to give it a notation, say [math]a\otimes b[/math], you would need to specify which one's the base and which one's the number you are plugging into the logarithm. If it was the case that the base is given the first number, then you'd have formulas like [math]a\otimes b+a\otimes c=a\otimes(bc)[/math] and [math]a\otimes(b^n)=n(a\otimes b)[/math] giving rise to a myriad of mistakes resulting from bad using of parentheses and an inevitable mistake [math]n(a\otimes b)=(na)\otimes b[/math] made by many. Similarly, such problems would arise by interchanging the roles of the left and right number, so we can forget a notation like that, people just don't learn.

Maybe, left exponentiation could be a thing, but it'd be very complicated to teach.

File: Untitled.png (8KB, 531x284px) Image search: [Google]

8KB, 531x284px

>>8815682
If you sift through the comments(I don't blame anyone for not doing this), some more compact derivatives of the notation are proposed.

The theme is to take three spaces that are distinguished by some means, then letting the output you are trying to reach be a space that is left empty. Like a/b\c, but the slashes could be any separation symbol.

>>8815694
If horizontal ordering is an issue, what about just going pure vertical? Power, root, and log written in a way similar to fractions. Like imagine the above example of a/b\c rotated 90 degrees counterclockwise. Power would be denoted by a with b encircled by separators above it. Root would be denoted by c with b encircled by separators below it. Log would be denoted by c above a, separated by double separators.

>>8815694
Left exponent would make things like [math](x^5)(y^3)[/math] very confusing

>>8815447

>>>/sqt/

You can rewrite all logarithms as an algebraic expression where the unknown is an exponent. You don't need a new symbol. This isn't a deep question. You don't need your own thread.