Here's the problem: Me and my teacher are having a discussion about the notation of a logarithm. My teacher says that the only way of notating a logarithm is like this:

$$^2\log\bigg(\frac 15\bigg)$$

I say that it is also possible to notate a logarithm in this form:

$$\log_2\bigg(\frac 15\bigg)$$

Of course, I'm just a student, so I don't know if I'm right or not. Can someone say if this is correct or not. Thanks a lot in advance!

  • $\begingroup$ Both are correct similar to $9,010$ in europe..is $9.010$ in the uk (or at least for me). I hate non-standard notation. $\endgroup$
    – Chinny84
    Dec 9, 2014 at 15:01
  • $\begingroup$ You are right and your teacher isn't! $\endgroup$
    – Alex Silva
    Dec 9, 2014 at 15:01
  • 2
    $\begingroup$ Where are you from? I haven't seen your teachers notation before? $\endgroup$
    – Alice Ryhl
    Dec 9, 2014 at 15:04
  • 1
    $\begingroup$ I have never seen the notation your teacher claims is the only way, but $\log_b$ is quite widely used. $\endgroup$ Dec 9, 2014 at 15:05
  • $\begingroup$ Well, I am from The Netherlands $\endgroup$
    – Adnan
    Dec 9, 2014 at 15:06

1 Answer 1


Notation is a matter of convention. In your case the notation $$\log_b a$$ is much (much) more common, but $${}^b \log a$$ is also a notation and you may or may not like and/or use it. If your teacher says that you must use his notation, you better do. Keep in mind that the one you prefer is more common for others, though.

A related example of convention is number formatting: One million and a half in US standard notation is $$1,\!000,\!000.5$$ and in european notation it is the other way around: $$1.000.000,\!5$$

Most computer parsing routines expect the US notation wich can lead to annoyances (because my numpad has a $,$ for example so I can't conveniently enter decimals for such applications via the numpad.

  • $\begingroup$ I do use the $^b\log a$ notation, because it's the notation my teacher uses. But on the test, I accidentally used the other notation because I am used to that notation. Not really smart of me $\endgroup$
    – Adnan
    Dec 9, 2014 at 15:12

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