To solve this inequality, we will use the properties of logarithms.

Given: log1/2 (3y-1) - log1/2 (3-y) < 0

By the properties of logarithms, we can combine the two logarithms into a single logarithm:

log1/2 [(3y-1)/(3-y)] < 0

Now, we need to solve for when the expression inside the logarithm is less than 0:

(3y-1)/(3-y) < 1

Multiplying both sides by (3-y) to get rid of the denominator:

3y - 1 < 3 - y

Adding y to both sides:

4y - 1 < 3

Adding 1 to both sides:

4y < 4

Dividing by 4:

y < 1

Therefore, the solution to the inequality log1/2 (3y-1) - log1/2 (3-y) < 0 is y < 1.