By capacitively charging an underdoped ultrathin La2-xSrxCuO4 film with an electric field applied across a gate insulator with a high dielectric constant, relative changes of the areal superfluid density ns of unprecedented strength were observed in measurements of the film kinetic inductance. Although ns appears to be substantially reduced by disorder, the data provide, for the first time on the same sample, direct compelling evidence for the Uemura relation Tc proportional to ns(T=0) in the underdoped regime of copper-oxide superconductors.