  We study the effect of a logarithmic nonlinearity in the Schr\"odinger
equation (SE) on the dynamics of a freely expanding Bose-Einstein condensate
(BEC). The logarithmic nonlinearity was one of the first proposed nonlinear
extensions to the SE which emphasized the conservation of important physical
properties of the linear theory, e.g.: the separability of noninteracting
states. Using this separability, we incorporate it into the description of a
BEC obeying a logarithmic Gross-Pittaevskii equation. We investigate the
dynamics of such BECs using variational and numerical methods and find that,
using experimental techniques like delta kick collimation, experiments with
extended free-fall times as available on microgravity platforms could be able
to lower the bound on the strength of the logarithmic nonlinearity by at least
one order of magnitude.
