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I have come across an usual convention for writing the square of the logarithm. It is $\log(x)^2$, which I would simply interpret as $\log(x^2)$. Now, the poster insists that $\log(x)^2$ is the same as $\log^2(x)$, and I am aware that this is at least correct in some programming language (I tried Python). Can anyone confirm this?

Edit: This question has been marked as duplicate based on similar questions asked around trigonometric functions, and those seem to confirm $\log(x)^2=(\log(x))^2$. As a follow up question, does that imply that $\log(1+x)^2=(\log(1+x))^2$?

Rebrado
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  • If you want the square of the logarithm, you should really offset with another set of parentheses, e.g. $(\log x)^2$. Cf. $\sin^2 x = (\sin x)^2.$ – Sean Roberson May 09 '23 at 00:17
  • I agree, but my question is, if you come across $\log(x)^2$, which one is it? – Rebrado May 09 '23 at 00:22
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    I think that this is essentially a duplicate of similar questions about trigonometric functions. Most people will likely interpret $\log(x)^2$ to mean $[\log(x)]^2$ (which is what I would understand $\log^2(x)$ to mean). But there is potential ambiguity. – Xander Henderson May 09 '23 at 00:31

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