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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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3  
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 at 19:16
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1 Answer

up vote 9 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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When there is only one variable in the argument, it is common to write $\log^2n$. –  Austin Mohr Mar 26 '12 at 0:22
    
How about for $ln$ (natural log), do most people use $ln^2(x)$ as well? –  Roronoa Zoro Mar 26 '12 at 0:26
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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
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@GerryMyerson "Grownups use log for the natural log." I believe most mathematicians is a more appropriate noun. –  000 Mar 26 '12 at 0:54
    
Wow, using $\log^2(n)$ to stand for $(\log n)^2$ seems terrible. It looks like function iteration, i.e. $\log \log n$. How do people know what they are talking about? Context? –  Ray Toal Jan 22 at 4:48
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