A logarithmic amplifier using current differencing trans-conductance amplifier (CDTA) is presented. Both current as well as voltage mode inputs are possible. Output can also be voltage or current. Owing to its current mode operation it consumes less power. Furthermore, the instability problem found in op-amp based logarithmic amplifiers due to the presence of an active element in the feedback loop is absent in the CDTA logarithmic amplifier. The simulation result confirms the logarithmic behavior with a very low-error. It also shows a good dynamic range.