This manuscript considers the initial boundary value problem for a pseudo-parabolic equation with logarithmic nonlinearity, which has been studied by Chen et al. (JDE, 2015, 258, 4424–4442). Under \(0 < {\mathcal J}(u_{0}) \leq d\) with \({\mathcal I}(u_{0}) < 0\) , we prove that any solution with positive energy must grow exponentially. Moreover, under \({\mathcal J}(u_{0}) \leq d\) with \({\mathcal I}(u_{0}) < 0\) , we prove that if there exists a time t0 ≥ 0 such that \({\mathcal J}(u(t_{0})) \leq 0\) , then this solution grows at least exponentially and at most bi-exponentially on [t0, +∞). The former resolves the indeterminacy of growth rate of solutions with positive energy under \(0 < {\mathcal J}(u_{0}) \leq d\) with \({\mathcal I}(u_{0}) < 0\) . The latter not only increases the lower bound function of the solutions from the previous polynomial growth to exponential growth, but also reduces the possibility of the growth rate from the trilateral uncertainty of either polynomial growth or exponential growth or bi-exponential growth to the dichotomous uncertainty of either exponential growth or bi-exponential growth under there exists a time t0 ≥ 0 such that \({\mathcal J}(u(t_{0})) \leq 0\) .
