In this article, we consider a semilinear pseudo parabolic heat equation
with the nonlinearity which is the product of logarithmic and polynomial
functions. Here we prove the global existence of solution to the problem
for arbitrary dimension $n \geq 1$ and power index
$p>1$. Asymptotic behaviour of the solution has been
addressed at different energy levels. Moreover, we prove that the global
solution indeed decays with an exponential rate. Finally, sufficient
conditions are provided under which blow up of solutions take place.