"Log Squared" (Not sure what to call this)

Question

What do you call something like log^2 x ("log squared x") and how would you calculate it? Just to be clear, I'm not referring to log-base-two of x or log x squared.

I have found contradictory answers online. One person says it's log x log x (not sure what that even means). Another person says that you take the log of the log of x, and yet another says that you square the log of x.

It's more like $$\log^2(x) = \left( \log(a) \log_a(x) \right)^2$$ — Bumblebee, Jun 06 '23 at 01:24
Welcome to MSE. It's not standard. Define it how you like. Just be sure to give a definition rather than assume your reader knows what you're talking about. Cf. this question — J. W. Tanner, Jun 06 '23 at 01:24
Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. — CrSb0001, Jun 06 '23 at 01:32

score 1 · Answer 1 · answered Jun 08 '23 at 10:28

There are two things this could be and you will need to look at the context to figure which is correct. Either, $\log^2 x = (\log x)^2$ (which is probably also the meaning of $\log x\,\log x$), or $\log^2 x = \log (\log x)$. Given this ambiguity, it’s better to avoid this notation yourself or to clearly define what you mean beforehand.

"Log Squared" (Not sure what to call this)

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