The notation $\exp(x)$ can be used in place of $e^x$, which is useful in two ways:
- For messy exponents, the former notation is more readable.
- It is useful to be able to describe the function $\exp$ in the abstract (as opposed to the value of that function at $x$).
Does a similar notation exist for $a^x$? Writing $\exp(x\log a)$ seems too cumbersome, so perhaps something like $\exp_a(x)$ is better.
Best Answer
Based on the comments:
I've used the notation myself in an undergraduate-level analysis manuscript.
Can't swear if I've seen $\exp_{a}$ used by other authors. By contrast, $\log_{a}$ is reasonably common in calculus books, and not uncommon in the literature, especially $\log_{2}$ and $\log_{10}$, but sometimes even $\log_{e}$.
In school many years ago, I recall books would create ad hoc named functions, similar to what Rob Arthan suggests, e.g., "Let $f(x) = b^{x}$...." Rogawski-Adams (the nearest calculus book at hand) does this, though they do use $\log_{b}$.
No matter what notation you settle on, the Right Way to handle the coding in LaTeX is to create and use a dedicated macro, e.g.,
\newcommand{\Exp}[1][]{\exp_{#1}}. If your journal or book series has style requirements, your manuscript can be made compliant by changing a single line of preamble code instead of by lengthy search-and-replace.