Where to write the power with a logarithmic function?

Question

This might be a simple question, but where would I write the power if I had a logarithmic function?

Instinctively I would write it as $\log^y(x)$. But I'm not sure if this is correct. Should I be writing $(\log(x))^y$ instead?

Thanks for the help!

Answer 1

Write $(\log x)^y$; you don't need more parentheses than that. There are problems with writing $\log^n\!x$. By analogy with (say) $\cos^n\!x$, it might be interpreted as $(\log x)^n$. However, it might also be taken to mean (quite logically) $\log...\log x$ (where there are $n$ applications of the logarithmic function).