While it is accepted that neutral densities in the thermosphere have a significant dependence on the solar soft X-ray fluxes, until recently the only coincident measurements available for an extended time period were from the AE-E satellite in the late 1970's. However, the Student Nitric Oxide Explorer (SNOE) satellite began measuring the solar soft X-ray flux (full disk) in March of 1998. Photometers on SNOE measured the solar flux in broad bands from 2 to 20 nm, rather than having high spectral resolution like the AE-E measurements. The SNOE measurements are coincident with high precision satellite orbit measurements, from which total neutral densities near 350 km can be derived, for the GeoForschungsZentrum (GFZ) satellite. The GFZ data ended on 1 June, 1999. A quantitative assessment of the relationship between densities and broad band measurements of solar soft X-rays, such as those from SNOE, is needed to determine the usefulness of broad band solar measurements for space weather applications. We have conducted such an assessment for geomagnetically undisturbed times and find correlations of ~0.74 between the daily variations in total neutral density and the soft X-rays measured by SNOE. The correlation seen between F10.7 and the neutral densities is significantly lower, ~0.60. These results indicate that broadband solar soft X-ray measurements could significantly improve the specification and prediction of neutral densities in the Earth's space environment.