Precise measurements were made of the differential length expansion (∆L'L'- ∆L0L0) and differential x-ray lattice-parameter expansions (∆a'a'- ∆a0a0), between specimens of pure aluminum and aluminum-base alloys containing 0.56 and 1.11 at.% magnesium, during slow reversible heating and cooling between the solidus and 185°C. The differential-expansion data are used to determine absolute differences between the equilibrium vacancy concentrations Cv in the dilute alloys and the pure metal from the relation ∆Cv=Cv'- Cv0=3(∆L'L'-∆L0L0)- 3(∆a'a'- ∆a0a0). Here ∆LL and ∆aa are length and lattice-parameter expansions, and the prime and zero superscripts refer to the alloy and pure aluminum, respectively. Since Cv0 is known from previous measurements, the vacancy concentrations in each alloy Cv' are then determined. The differential length and lattice-parameter measurements were carried out using the same technique previously employed in the determination of equilibrium vacancy concentrations in dilute aluminum-silver alloys. The technique allows the measurement of concentration differences as small as +/-4×10-5. The addition of magnesium caused only exceedingly small changes in the equilibrium vacancy concentrations. The changes did not exceed a few percent of the concentrations in pure aluminum. The results are compared at 650°C to the simple first-order vacancy-solute-atom-binding model of Lidiard and others. It is concluded that the vacancy-magnesium-atom binding free energy was Gv,Mgb(650°C)𕲘.01 eV. Possible values of binding energies and entropies consistent with these results are discussed. The results are compared to the previous measurements for dilute aluminum-silver alloys where larger (but still small) solute-induced vacancy increments were found, and where Gv,Agb(650°C)~0.08 eV.