g $\frac{1}{2} \log _{2} x=\frac{1}{3} \log _{2} y-1$

Step 1 ：Given the logarithmic equation \(g \frac{1}{2} \log _{2} x=\frac{1}{3} \log _{2} y-1\).

Step 2 ：Isolate the variable on one side of the equation. However, the equation contains two variables, x and y. Without additional information, we can't solve for a specific value of x or y. But we can express one variable in terms of the other.

Step 3 ：Rearrange the equation to isolate x: \(x = 0.25y^{2/3}\)

Step 4 ：Final Answer: \(\boxed{0.25y^{2/3}}\)