Solve the equation: $\;$ $2^{\frac{3}{\log_2 x}} = \dfrac{1}{64}$
Given equation: $\;\;$ $2^{\frac{3}{\log_2 x}} = \dfrac{1}{64}$
i.e. $\;$ $2^{\frac{3}{\log_2 x}} = 2^{-6}$
i.e. $\;$ $\dfrac{3}{\log_2 x} = -6$
i.e. $\;$ $-2 = \dfrac{1}{\log_2 x}$
i.e. $\;$ $\log_2 x = \dfrac{-1}{2}$
i.e. $\;$ $x = 2^{\frac{-1}{2}} = \dfrac{1}{\sqrt{2}}$