In this work we investigate asymptotic stability and instability at infinity of solutions to a logarithmic wave equation utt-Delta u+u+(g*Delta u)(t)+h(ut)ut+|u|2u=ulog|u|k,in an open bounded domain omega subset of R3 whith h(s)=k0+k1|s|m-1We prove a general stability of solutions which improves and extends some previous studies such as the one by Hu et al. (Appl Math Optim, https://doi.org/ 10.1007/s00245- 017-9423-3) in the case g = 0 and in presence of linear frictional damping ut when the cubic term |u|2u is replaced with u. In the case k1 = 0, we also prove that the solutions will grow up as an exponential function. Our result shows that the memory kernel g dose not need to satisfy some restrictive conditions to cause the unboundedness of solutions.