Notation of logarithms

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!

• 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. Dec 9, 2014 at 15:01
• You are right and your teacher isn't! Dec 9, 2014 at 15:01
• Where are you from? I haven't seen your teachers notation before? Dec 9, 2014 at 15:04
• I have never seen the notation your teacher claims is the only way, but $\log_b$ is quite widely used. Dec 9, 2014 at 15:05
• Well, I am from The Netherlands Dec 9, 2014 at 15:06

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.
• 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 Dec 9, 2014 at 15:12