What would be the correct notation of antilogarithm if I would also like to specify the base? In my high school days, my teacher told me that $\mathrm{antilog}( x)$ is the same as $10^x$ and $e^x$ is the same as $\exp x$. While the latter is true, I can't say for sure whether the former is true. After looking it up on Google, I didn't find a single source claiming $\mathrm{antilog} (x) \equiv 10^x$. 
So if what I think is correct, how would I specify the base while using antilogarithm. 
For example : We usually write the base $10$ logarithm as $\log x$ when the context is clear. However, we can clarify this notation as, $\log_{10} x$, how can I make base $10$ antilogarithm specific and clear the same way? I'm asking for a correct notation.
My ideas : Writing $4^x$ as $\log^{-1}_4 x$ 
But I'm looking for something like $\mathrm{antilog}_4 (x) $, is this a correct a notation?
 A: Most people will probably be able to guess what you mean by $\operatorname{antilog}_4(x)$, but in general it's a really bad idea to use notation that doesn't fall in either of these categories


*

*Universally accepted - i.e. people will think you're mad if you define what $a+b$ means (especially if you define it to mean something different from what it usually means - the exception being if you're writing an introductory text and want to make a point about notation)

*Generally understood to mean a specific thing among anybody that might get to read your text - e.g. at the math institute of my university $\log$ was generally understood to mean (what we called) the natural logarithm (i.e. the logarithm with base $e$), so for homework-style papers that was likely ever to be read by our professors or fellow students, it made sense not to define that. 

*Something you've defined
As my example in group 2 shows, you have to be careful before deeming some notation to be universally accepted, this particular subject can give rise to many examples, another being $\lg x$, which (as you can read from the comments to the question) some use to mean $\log_2 x$ and others to mean $\log_{10} x$, the only two bits of notation I think (and that will probably attract comments telling me I'm wrong) you can be fairly sure is universally understood in this area is $b^x$ and $\log_b x$.
Another thing brought up in the comments is that notation for inverses of functions is not as universally understood as one might think, $f^{-1}(x)$ might to some mean the inverse of $f(x)$ and to others $\frac{1}{f(x)}$.
But what do you need this for, is there any reason to not just write $4^x$.
