Grade 11 2020 Problem 4

Odredi sva realna rješenja jednadžbe

$$\log_2 x \cdot \log_4 x + \log_4 x \cdot \log_8 x + \cdots + \log_{2^{2019}} x \cdot \log_{2^{2020}} x = \frac{2019}{2020}.$$