  The $\gamma$-ray strength functions and level densities of $^{73,74}$Ge have
been extracted up to the neutron separation energy S$_n$ from particle-$\gamma$
coincidence data using the Oslo method. Moreover, the $\gamma$-ray strength
function of $^{74}$Ge above S$_n$ has been determined from photo-neutron
measurements, hence these two experiments cover the range of E$_\gamma \approx$
1-13 MeV for $^{74}$Ge. The obtained data show that both $^{73,74}$Ge display
an increase in strength at low $\gamma$ energies. The experimental $\gamma$-ray
strength functions are compared with $M1$ strength functions deduced from
average $B(M1)$ values calculated within the shell model for a large number of
transitions. The observed low-energy enhancements in $^{73,74}$Ge are adopted
in the calculations of the $^{72,73}$Ge(n,$\gamma$) cross sections, where there
are no direct experimental data. Calculated reaction rates for more
neutron-rich germanium isotopes are shown to be strongly dependent on the
presence of the low-energy enhancement.
