In this paper, a new design procedure has been proposed for realization of logarithmic function via three phases: 1) differentiation; 2) division; and 3) integration for any arbitrary analog signal. All the basic building blocks, i.e., differentiator, divider, and integrator, are realized by operational transconductance amplifier, a current mode device. Realization of exponential, power law, and hyperbolic function as the design examples claims that the proposed synthesis procedure has the potential to design a log-based nonlinear system in a systematic and hierarchical manner. The performance of all the proposed circuits has been verified with SPICE simulation.