  Logarithmic superfluid theory of physical vacuum suggests that gravity has a
multiple-scale structure; where one can recognize sub-Newtonian, Newtonian,
logarithmic, linear and quadratic (de Sitter) terms in the induced spacetime
metric and effective potential. To test the theory's predictions on a galactic
scale, we apply best-fitting procedures to the rotation curve data obtained
from fifteen galaxies by the HI Nearby Galaxy Survey; assuming their stellar
disk's parameters to be fixed to the mean values measured using photometric
methods. Although the fitting results seem to be sensitive to a stellar disk
model chosen, they correspond closely with observational data, even for those
galaxies which rotation velocity profiles do not have flat regions.
