Solving $2\log_2 (\log_2 x) + \log_{1/2} (\log_2 x) = 1$

Question

just looking for some help with the following:

$$2\log_2 (\log_2 x) + \log_{1/2} (\log_2 x) = 1$$

I know how to solve a log equation with a single nested log that's $= 1$ or $0$ or some number, but I'm unsure of what to do when summing/ subtracting nested logs like these.

If possible, a hint would be much more appreciated than the flat out answer.

Thanks in advance to anyone who stops to help.

Answer 1

I would first perform a change of basis in the second term.

Recall: $\log_{(1/2)}a = \frac{\log_2(a)}{\log_2(1/2)}$

(Of course, then see that $1/2 = 2^{-1}$)