Notation of logarithms

Question

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. — Chinny84, Dec 09 '14 at 15:01
Where are you from? I haven't seen your teachers notation before? — Alice Ryhl, Dec 09 '14 at 15:04
I have never seen the notation your teacher claims is the only way, but $\log_b$ is quite widely used. — Henrik supports the community, Dec 09 '14 at 15:05
@MaMing $c{\ }^a\lg b$, you need to include spacing in the markup, though ;) — AlexR, Dec 09 '14 at 15:08
You can cheat and write $\frac {\ln \frac 15}{\ln 2}$ which is how'd you evaluate it on a calculator anyway. — GFauxPas, Dec 09 '14 at 15:34
As far as I can tell, the notation $^b\log$ is used in the Netherlands and in Indonesia. That it's the only notation is very questionable, as the rest of the world doesn't use it. — egreg, Dec 09 '14 at 15:43

score 4 · Accepted Answer · answered Dec 09 '14 at 15:04

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 — Adnan, Dec 09 '14 at 15:12

Notation of logarithms

1 Answers1