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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?

Yanko
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William
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  • Whatever notation is correct as long as you take your time to define it. So if you introduce $\mathrm{antilog}_a (x) \equiv a^x$ nobody will complain. – N74 Sep 15 '18 at 09:09
  • @N74 Sure, but I'm looking for a "widely-known" kinda notation so that I wouldn't have to define it. – William Sep 15 '18 at 09:10
  • You will have bad luck: some days ago, on this site, I read a question about the $\exp$ notation. Take the vectors, in example: many use a bold notation, others use an arrow over the name and so on... it's always better to define what you mean when you write. – N74 Sep 15 '18 at 09:15
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    Even though I've only encountered $\operatorname{antilog}$ very few times, I would guess that $\operatorname{antilog}_4(x)$ was a cumbersome notation for $4^x$. But I think you should always define any kind of notation related to this concept, the only notation you can be fairly sure is universally understood is $4^x$. Even with $\log x$ you can encounter confusion, at university we mostly used that for the natural logarithm(with base $e$). – Henrik supports the community Sep 15 '18 at 09:21
  • I have sometimes seen $\lg x$ being used for $\log_{10} x$ – Mandelbrot Sep 15 '18 at 09:24
  • And I've seen that ($\operatorname{lg} x$) used for $\log_2 x$, just another example of why you need to define almost anything in this area. - Unless you're writing for a very small specific audience - I didn't waste space defining $\log$ to mean the natural logarithm when I handed in homework-style papers at university, it was so general there that it felt unneeded, I did however define $a^{\underline{n}}$ when I used that, because I had seen several meanings of that (and other notation for the meaning I intended). – Henrik supports the community Sep 15 '18 at 09:34
  • For what purposes do you need this? Any mathematician will understand both notations (the first one might be a little confusing with the inverse $a^{-1}=\frac{1}{a}$ though). – Yanko Sep 15 '18 at 09:38
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    How is $10^x$ not satisfactory? It is certainly completely unambiguous. – hmakholm left over Monica Sep 15 '18 at 10:08

1 Answers1

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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

  1. 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)

  2. 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.

  3. 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 $4^x$.

Henrik supports the community
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