Is there a convention to express: $~\log(\log(x))~$?

Question

I am doing a high order log transformation (e.g. $\log(\log{X+1}) = X_t$) but don't know how to express it concisely. Is there a convention I can use to express the order of a log transformation?

Answer 1

I could be wrong, and it's been less than 24 hours since you posted your question, but the fact that no one in the community seems to know of such a mathematical symbol indicates that there probably isn't any common notation for what you're after.

In any case, making mathematical symbols go from 11 characters to 6 characters - or whatever - should be the least of your worries as a mathematician. Although, if you're into concise programming, then I can see why you asked your question- but I doubt most programming languages have a common symbol for what you're after.

I like to be as clear and unambiguous as possible, and I try not to sacrifice clarity for some fewer characters.

So just write $\log(\log(x))$, and if the order is of say, 30, you can write:

"$\log(\log(...\log(\log(x))))\ $ where there are $30 \ (nested)\ \log$s."