  We examine inflationary universe models driven by scalar fields with
logarithmic potentials of the form $V(\phi) = V_0 \phi^p(\ln \phi)^q$.
Combining the slow-roll approximation with asymptotic techniques, we identify
regions of the potential where inflation may occur and obtain analytic
expressions for the evolution of the field and the metric in these cases. We
construct a family of exact solutions to the equations of motion with
potentials resembling the above form and demonstrate their inflationary nature;
deflationary and conflationary cosmological behaviours are also defined and
identified. Finally, a computation of scalar density and tensor gravitational
perturbations produced by the model is presented.
