What does a superscript after log mean?

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In this paper they mention an algorithm has big-O time complexity of $O(\log^4n)$, what does the $\log^4$ mean? I understand $\log_4x$ is the log with base 4 of x.

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As mentioned by another user already this must be an exponent. The only exception where a superscript would be used for a logarithm to denote the base is as follows: $^4 log(n)$, which means log base 4.