We analyse the scaling properties of turbulent flows using a suite of three-dimensional numerical simulations. We model driven, compressible, isothermal, turbulence with Mach numbersranging from the subsonic (M≈ 0.5) to the highly supersonic regime (M≈ 16). The forcingscheme consists of both solenoidal (transverse) and compressive (longitudinal) modes inequal parts. We confirm the relation σ2s= ln (1 + b2M2) between the Mach number and thestandard deviation of the logarithmic density with b = 0.33. We find increasing deviationswith higher Mach number from the predicted lognormal shape in the high-density wing ofthe density probability density function. The density spectra follow D(k, M) ∝ kζ (M) withscaling exponents depending on the Mach number. We find ζ (M) = αMβ with coefficientsα = −2.1 and β = −0.33. The dependence of the scaling exponent on the Mach numberimplies a fractal dimension D = 2 + 1.05M−0.33.