  It is known that almost all approaches to quantum gravity produce a
logarithmic correction term to the entropy of a black hole, but the exact
coefficient of such a term varies between the different approach to quantum
gravity. Such logarithmic terms can also occur due to thermal fluctuations in
both analogous and real black holes so that we will analyze the effects of
logarithmic corrections term with variable coefficient on properties of
analogous black hole. As these properties can be experimentally tested, they
can be used to obtain the correct coefficient for such terms for an analogous
black hole. We will argue that as even the real black holes can be considered
as thermodynamical objects in Jacobson formalism, so such analogous black holes
can be used to obtain the correct coefficient for the real black holes, and
this in turn can be used to select the correct approach to quantum gravity. In
that case, we use an adaptive model of graphene, which is still far from real
graphene, to investigate some thermodynamics quantities of BTZ black hole.
