The logarithmic part of the Lamb shift, the contribution of the relative order a₃log (1/a) to the atomic state energy, is related to the usual infrared divergence. This fact allows one to calculate easily such corrections in positronium, and derive the recoil and electron-electron terms in the Lamb- shift Hamiltonian in many-electron atoms. Logarithmic energy corrections of the next order, a4 log (1/a), are of a different, relativistic nature. Their calculation is reduced to the ordinary perturbation theory for the nonrelativistic Schrodinger equation. The perturbation operators have the Breittype structure and are found by the calculation of on-mass-shell diagrams. For positronium, the calculated log-arithmic correction survives only in n3Sj states and constitutes ¿ma6 log (l/a)/n3. Logarithmic corrections of the relative order a2 log (1/a) to the positronium decay rate are also of the relativistic origin and can be easily computed within the same approach. Arguments are presented in favour of a large numerical factor in the (a/rc)2 correction to the positronium decay rate.