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!
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.