We consider logarithmic contributions to the free energy, instanton effective action, and Laplace sum rules in QCD that are a consequence of radiative corrections. Upon summing these contributions by using the renormalization group, all dependence on the renormalization scale parameter μ cancels. The renormalization scheme dependence in these processes is examined, and a renormalization scheme is found in which the effect of higher-order radiative corrections is absorbed by the behaviour of the running coupling.