We discuss the existence and multiplicity of solutions for logarithmic Schrodinger equations with potential. Since the corresponding functional is not well defined in $H^1(\R^N)$, by imposing some conditions on $V(x)$, we first prove that the functional is well defined in a subspace of $H^1(\R^N)$. Then, two sequence of solutions are obtained by variational methods: one sequence is diverging to infinity while the other one converging to zero.