Solving equation $\log_y(\log_y(x))= \log_n(x)$ for $n$ I'm just wondering, if I log a constant twice with the same base $y$,
$$\log_y(\log_y(x))= \log_n(x)$$
Can it be equivalent to logging the same constant with base $n$? If yes, what is variable $n$ equivalent to?

Yes you can do that with the initial conditions for a logarithm satisfying.
The conditions for log(x) to the base n  are: x > 0, n > 0 and n != 1.
so you should be careful with the domain that you are choosing.
