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

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

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not matter of $\textbf{correct}$ it is a matter of which is more $\bf{conventional}$, and to answer it: $\log^2(n)$. – Daniel Montealegre Mar 26 '12 at 0:18
Does the same go for $ln$? – Roronoa Zoro Mar 26 '12 at 0:20
Better be clear than rely on conventions if you think you might be misunderstood. – lhf Mar 26 '12 at 0:26
@RoronoaZoro Yes, the same goes for $\ln^2(x)$ and $\big(\ln(x)\big)^2$. – user93957 Jan 22 '14 at 19:16
up vote 12 down vote accepted

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 $\bigl(\log(n)\bigr)^2$

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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 $\log_{10}$. – Gerry Myerson Mar 26 '12 at 0:48
@GerryMyerson "Grownups use log for the natural log." I believe most mathematicians is a more appropriate noun. – 000 Mar 26 '12 at 0:54
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. – Ray Toal Jan 22 '14 at 23:47
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. – Soke Jan 26 '14 at 16:30
@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 $\log\log\log\log x$. – Gerry Myerson Jul 17 '14 at 23:51

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