Where am I going wrong on this integrated rate law problem?

The integrated rate law ln([A]ₜ/[A]ₒ) = -kt that you used is just for first order reactions.
However, the reaction in the question is second order.

The integrated rate law for the second order reaction:
1/[A]ₜ = kt + (1/[A]ₒ)
1/[A]ₜ = (0.543 M⁻¹ s⁻¹) × (30.0 × 60.0 s) + (1/0.0500 M⁻¹)
1/[A]ₜ = 997.4 M⁻¹
Remaining concentration after 30.0 min, [A]ₜ = 1/997.4 M = 0.00100 M

For second order reaction, 1/A = 1/Ao + Kt
where A = concentration of reactant at any time t.
Ao = Initial concentration of reactant ( at time t = 0)
K = specific rate constant and t = time taken for the reaction.

1/A = 1/0.050M + (0.543M^-1S^-1 x 1800sec)
1/A = 20 + 977.4 = 997.4
Hence A = 0.001M

as the reaction is the second order, you must put [0.0500]^2