  We investigate conditions for logarithmic complete monotonicity of product
ratios of gamma and q-gamma functions whose arguments are linear functions of
the variable. We give necessary and sufficient conditions in terms of
nonnegativity of a certain explicitly written measure in the q case and of a
certain elementary function in the classical q=1 case. In the latter case we
further provide simple new sufficient conditions leading to many new examples
of logarithmically completely monotonic gamma ratios. Finally, we apply some of
our results to study monotonicity of some gamma ratios and rational functions.
