In this work, we show that two competing equations of state, the first one derived from some effective approximation of intermolecular potential suspected to be responsible for so-called "thermodynamic scaling" and the second one following from the definition of isothermal bulk modulus, are able to describe very well experimental volumetric data of supercooled van der Waals liquids in the thermodynamic scaling regime. The values of the exponent gamma(EOS) experimentally established from both these equations of state are numerically very close, and moreover they enable us to achieve a high quality of the specific volume or density linear scaling suggested by these equations. However, the found density scaling requires a distinctly different value of gamma(EOS) than that leading to the scaling of dynamic quantities. The discrepancy can be explained by our modification of the Avramov model which assumes the density scaling of the maximal energy barrier with the scaling exponent gamma(EOS).