In this paper, we propose a configurable rotation matrix for Hyperbolic COordinate Rotation DIgital Computer (CORDIC) to compute any logarithm and inverse logarithm. The rotation matrix of the conventional Hyperbolic CORDIC computes only natural logarithm and natural inverse logarithm whereas the proposed rotation matrix configures the Hyperbolic CORDIC to compute any logarithm and inverse logarithm. Subsequently, an architecture for configurable Hyperbolic CORDIC has been designed based on the proposed rotation matrix. An extensive vector matching is performed to validate the proposed architecture. Finally, an ASIC implementation for configurable Hyperbolic CORDIC has been performed using TSMC 45-nm CMOS technology @ 1 GHz frequency. The accuracy of the proposed configurable Hyperbolic CORDIC is same as conventional Hyperbolic CORDIC. The proposed approach saves 19.22% on chip area and 17.52% power consumption for decimal logarithm computation and 18.55% on chip area and 16.12% power consumption for inverse logarithm computation when compared with the state of the art approaches. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.