# Do powers of logarithm arise naturally in any physical equation? [closed]

Everything that we learned in the school maths I've come to use at one time or another. Except one thing. Solving equations like this:

$$1 + \log_2^2 x = \log_2 8x$$

"Where do we use this in real life?" Is this an example of an actually useless piece of school maths or have I not come across the real life use yet?

I am not sure why, but raising a logarithm to a power (other than 1 or 0) seems inherently unphysical to me.

## closed as too broad by Qmechanic♦May 15 at 12:35

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• Powers of logarithms are not unphysical at all. For example, they arise when renormalizing physical quantities in quantum field theories, as in equation (40) here: pdfs.semanticscholar.org/c6cd/… – G. Smith May 15 at 16:22