I am not sure if I know what you really want to know. So, I apologize if my answer does not correspond to your question.
Not specifically in rheology, but in general, if the plot logA vs. logB is linear, a power law is evidently inferred A=aB^b. In the paper that you attached, in the paragraph marked in yellow authors claimed power law for the dependence of viscosity vs. concentration based upon this single fact.