Answer:
[tex]\bold{y=\dfrac{\sqrt[3]{\bold x}}x=\bold \big x^{-\frac23} }[/tex]
Step-by-step explanation:
[tex]\log_2x=\dfrac3{\log_{xy}2}\qquad\qquad\qquad\quad x>0\,,\ y>0\\\\\\\log_2x=3\cdot\dfrac1{\log_{xy}2}\\\\\\\log_2x=3\cdo\log_2(xy)\\\\\log_2x=\log_2(xy)^3\quad\iff\quad x=(xy)^3\\\\x=x^3y^3\\\\\dfrac{x}{x^3}=y^3\\\\y=\sqrt[\big3]{\dfrac{x}{x^3}}\\\\y=\dfrac{\sqrt[3]x}x[/tex]
{or: [tex]\dfrac{x}{x^3}=y^3\quad \implies\quad y=\left(\dfrac{x}{x^3}\right)^\frac13=\left(\big x^{-2}\right)^\frac13=\big x^{-\frac23}[/tex]}
