  X-ray studies of normal late-type galaxies have shown that non-nuclear X-ray
emission is typically dominated by X-ray binaries, and provides a useful
measure of star formation activity. We have modeled the X-ray evolution of
late-type galaxies over the $\sim$ 14 Gyr of cosmic history, with an
evolutionary population synthesis code developed by Hurley et al. Our
calculations reveal a decrease of the X-ray luminosity-to-mass ratio $L_{\rm
X}/M$ with time, in agreement with observations (Fig.~7$a$). We show that this
decrease is a natural consequence of stellar and binary evolution and mass
accumulating process in galaxies. The X-ray-to-optical luminosity ratio $L_{\rm
X}/L_{\rm B}$ is found to be fairly constant (around $\sim 10^{30}$
erg\,s$^{-1}$$L_{\rm B,\odot}^{-1}$, Fig.~7$b$), and insensitive to the star
formation history in the galaxies. The nearly constant value of $L_{\rm
X}/L_{\rm B}$ is in conflict with the observed increase in $L_{\rm X}/L_{\rm
B}$ from $z=0$ to 1.4. The discrepancy may be caused by intense obscured star
formation activity that leads to nonlinear relationship between X-ray and
B-band emission.
