1) To solve the inequality log2 x > 2, we can rewrite it in exponential form: 2^2 < x.
This simplifies to 4 < x.

2) To solve the inequality log1/5 (x+2) ≥ -1, we can rewrite it in exponential form:
1/5^(-1) ≤ x+2. This simplifies to 5 ≤ x+2, which means x ≥ 3.

3) To solve the inequality log5 x > log5 (3x-4), we can cancel out the logarithms since they have the same base:
x > 3x-4. By solving for x, we get x < 4.

Therefore, the solution to the system of inequalities is 4 < x and x ≥ 3.