In this talk, we prove the uniform Hausdorff dimension of the inverse images of a large class of symmetric Levy processes with weak scaling conditions on their characteristic exponents. Along the way we also prove an upper bound for the uniform modulus of continuity of the local times of these processes. This result extends a result of Kaufman (1985) for Brownian motions and of Song, Xiao, and Yang (2018) for stable processes. We also establish the packing dimension results as a byproduct.