The invention relates to a logarithmic amplifier with high precision, low power consumption and large dynamic range. The logarithmic amplifier comprises a voltage-current converting input stage, a current-voltage converting output stage and a constant-current source. The logarithmic amplifier is characterized in that the voltage-current converting input stage is composed of five-stage linear logarithmic amplifiers in a cascading manner, each stage of linear logarithmic amplifier contains an amplification stage and a transconductance stage, and the output current of each transconductance stage is converted to output voltage through the current-voltage converting output stage so as to provide the biased constant-current source, frequency compensation and the like for the circuit. Each stage of amplification factor of the logarithmic amplifier is reasonably designed, thus increasing the dynamic range of the circuit; the constant-current source is elaborately designed, thus increasing logarithmic precision, reducing the power consumption of the circuit; and a detuning adjustment end and a slope adjustment end are stalled. The logarithmic amplifier of the invention is characterized by small size, wide dynamic range, low power consumption, high precision, flexible operation and the like.