  We compute logarithmic corrections to the black hole entropy $S_{\rm bh}$ in
a holographic set up where the cosmological constant $\Lambda$ and Newton's
constant $G_D$ are taken to be thermodynamic parameters, related to variations
in bulk pressure \(P\) and central charge \(c\). In the bulk, the logarithmic
corrections are of the form: $\mathcal{S} = S_{\rm bh} - k \ln S_{\rm bh} +
\cdots$ arising due to fluctuations in thermodynamic volume, induced by a
variable $\Lambda$, in addition to energy fluctuations. We explicitly compute
this coefficient $k$ for the BTZ black hole and show that the result matches
with the one coming from the logarithmic corrections to the Cardy's formula. We
propose an entropy function in the CFT, which exactly reproduces the
logarithmic corrections to black hole entropy in arbitrary dimensions.
