  Tracking the star formation rate to high redshifts requires knowledge of the
contribution from both optically visible and obscured sources. The dusty,
optically-obscured galaxies can be located by X-ray and infrared surveys. To
establish criteria for selecting such sources based only on X-ray and infrared
surveys, we determine the ratio of infrared to X-ray brightness that would be
observed by SIRTF and Chandra for objects with the same spectral shapes as
nearby starbursts if seen at high redshift. The parameter IR/X is defined as
IR/X = (flux density observed in SIRTF MIPS 24 $\mu$m filter in mJy)/(total
flux observed within 0.5-2.0 keV in units of 10^-16 ergs\s\cm^2). Based on
observations of NGC 4038/39 (``The Antennae''), NGC 3690+IC 694 (Arp 299 or Mkn
171), M 82, and Arp 220, nine starburst regions are compared using mid-infrared
spectra taken by the Infrared Space Observatory (ISO) and X-ray spectra
obtained with Chandra . The IR/X are determined as they would appear for 1<z<3.
The mean IR/X over this redshift range is 1.3 and is not a significant function
of redshift or luminosity, indicating that SIRTF surveys reaching 0.4 mJy at 24
$\mu$m should detect the same starbursts as deep CXO surveys detect at a flux
of 0.3x10^-16 ergs/s/cm^2. The lower bound of IR/X for starbursts is about 0.2,
suggesting that objects with IR/X smaller than this have an AGN X-ray component
in addition to the starburst. Values of IR/X for the obscured AGN within NGC
1068, the Circinus galaxy, and NGC 6240 are also determined for comparison
although interpretation is complicated by the circumnuclear starbursts in these
galaxies. Any sources found in surveys having IR/X>4 would not match any of the
objects considered.
