I ran across these two notations for the log function (squared), which one is more conventional.

$\log^2(n)$ or $[\log(n)]^2$

  • 3
    $\begingroup$ not matter of $\textbf{correct}$ it is a matter of which is more $\bf{conventional}$, and to answer it: $\log^2(n)$. $\endgroup$ Mar 26, 2012 at 0:18
  • $\begingroup$ Does the same go for $ln$? $\endgroup$ Mar 26, 2012 at 0:20
  • $\begingroup$ Better be clear than rely on conventions if you think you might be misunderstood. $\endgroup$
    – lhf
    Mar 26, 2012 at 0:26
  • $\begingroup$ @RoronoaZoro Yes, the same goes for $\ln^2(x)$ and $\big(\ln(x)\big)^2$. $\endgroup$
    – user93957
    Jan 22, 2014 at 19:16

1 Answer 1


Most people will use $\log^2(n)$ and there is no problem with that. If you want to be absolutely certain no one will think you are talking about $\log\log n$, then you can write $\bigl(\log(n)\bigr)^2$

  • 9
    $\begingroup$ Grownups use $\log$ for the natural log. If you want to be absolutely certain that no one will think you are talking about common logartihms, you can use $\ln$. If for some reason you want to talk about common logs and you want to be certain no one will misunderstand, you can write $\log_{10}$. $\endgroup$ Mar 26, 2012 at 0:48
  • 12
    $\begingroup$ @GerryMyerson "Grownups use log for the natural log." I believe most mathematicians is a more appropriate noun. $\endgroup$
    – 000
    Mar 26, 2012 at 0:54
  • 1
    $\begingroup$ Interesting, and thank you. That bothers me no end, though. It bothered Babbage, too, from what I understand, at least if one believes what Wikipedians have written about Abuse of Notation. $\endgroup$
    – Ray Toal
    Jan 22, 2014 at 23:47
  • 1
    $\begingroup$ There's a lot of notation inconsistencies. $f^2 (n)$ usually means $f(f(n))$ not $f(n)^2$, yet $\sin^2 x$ means $(\sin x)^2$. IMO it boils down to the fact that $\log \log x$ is not very commonly used, and $\sin \sin x$ (as far as I know) makes no sense to ever use since $\sin x$ puts in an angle and gives you a ratio, so you would be giving a ratio to be interpreted as an angle to give a ratio. $\endgroup$
    – MCT
    Jan 26, 2014 at 16:30
  • 4
    $\begingroup$ @MichaelT, "$\log\log x$ is not very commonly used" --- this will come as news to fans of Analytic Number Theory, who have grown accustomed to that and $\log\log\log x$, and even $\log\log\log\log x$. $\endgroup$ Jul 17, 2014 at 23:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.