Writing Math: Is using both $e^x$ and $\exp(x)$ ok for longer works?

Question

I wanted to know what you guys think about mixing both notations for the exponential function $e^x$(for simple argument and to save space for larger equations) and $\exp(x)$ (for more complicated arguments) in one single work.

Answer 1

Unfortunately I discovered that I've mixed the notation in a work on Lie Groups.

It was unfortunated because I than realized that I could use $exp(X)$ for the application between the Lie Algebra and the Lie Group, while using $e^X$ for the proper matrix exponential and then I could conclude in a theorem that $exp(X)=e^X$. It would have been a great theorem...