20. $\frac{\log _{2} x}{\log _{2}^{2} a}-\frac{2 \log _{a} x}{\log _{\frac{1}{b}} a}=\log _{\sqrt[3]{a}} x \cdot \log _{a} x$.
20. Transitioning to logarithms with base 2, we get

$$
3\left(\log _{2}:\right)^{2}-\log _{2} x\left(1+2 \log _{2} h\right)=0, \quad x>0 . \text { From which } x_{1}=1, \quad x_{2}=\sqrt[3]{2 b^{2}} .
$$