  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 $\mu$ 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.
