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.
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.