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I want to write an exponential function with base other than e in my paper, where the power is a complex equation. I can't write it as $b^{f(x)}$, because f(x) is a complex equation and it looks bad. I want to write it in a manner similar to when we use 'e' as a base (like $\exp(f(x))$). I want to know can I write it as $\exp(b,f(x))$?

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    In principle, if you state what you mean, you could do it any way you want (so long as it's clear). – SvanN Jun 22 '17 at 07:17
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    An alternative is $b^{f(x)}=\exp(\log_e(b),f(x))$ – Henry Jun 22 '17 at 07:23
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    I would think $\exp_b(f(x))$ looks nicer, and coincides with the notation $\log_b$. But you would probably have to say what you mean the first time you use it. – Arthur Jun 22 '17 at 07:52

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What you have suggested $\exp(b,f(x))$ is somewhat unconventional.

Henry's suggestion in the comment is correct in that it uses completely standard notation so is to be favoured compared to your suggestion.

A little more compact than that is $b^{f(x)}=\exp(\ln(b)\,f(x))$

An alternative would be to clearly define your complicated $f(x)$

$f(x)=\ldots\,$ and continue to use $b^{f(x)}$ which is tidy and without ambiguity.

e.g.your paper might contain: $$ f(x) = \textrm{some large and complicated equation} $$

"Consider the expression $b^{f(x)}$ where $f(x)$ is given above $....$"

Or you could use Knuth's up arrow notation $$ b \uparrow f(x) $$

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