Resolver em $\mathbb{R}$: $\left(\log_x 2\right)\left(\log_{\frac{x}{16}} 2\right) = \log_{\frac{x}{64}} 2$.

$\dfrac{1}{\left(\log_2 x\right)\left(\log_2 \dfrac{x}{16}\right)} = \dfrac{1}{\log_2 \dfrac{x}{64}}\ \Rightarrow\ \left(\log_2 x\right)\left[\left(\log_2 x\right) - 4\right] = \left(\log_2 x\right) - 6\ \Rightarrow$

 

$\Rightarrow\ \log_2 x = 2\ \vee\ \log_2 x = 3\ \Rightarrow\ x = 4\ \vee\ x = 8$

$\fbox{$S = \{4,\ 8\}$}$