  We consider three-loop radiative-recoil corrections to hyperfine splitting in
muonium generated by the gauge invariant set of diagrams with virtual
light-by-light scattering block. These corrections are enhanced by the large
logarithms of the electron-muon mass ratio. We present the results of an
analytic calculation of the single-logarithmic radiative-recoil corrections of
order $\alpha^2(Z\alpha)(m/M)E_F$ to hyperfine splitting in muonium generated
by these diagrams.
