The investigation of the power efficiency of the linear Gm - C integrator and the log - domain integrator is given. It is shown that log- domain filters are better suited for low-power signal processing at low supply voltages. The simulations show that the log -domain integrator has lower distortion than the linear Gm - C integrator. The log-domain circuits are appropriate for the filter designs with the low-voltage ,low -power, high frequency and low distortion.