Logarithmic amplifier is realized with op-amp is given in figure bellow.
Logarithmic amplifier provides a logarithmic output for a linear voltage input. In the given schematic, output voltage can be calculated via equaling currents. Input current is
Current IIN flows through diode D. I-V characteristic of the diode is
In here, IS is the saturation current, VT is the thermal voltage and VD is diode voltage.
It means that
Input voltage is positive, and output voltage is negative natural logarithm scaled.
Go to logarithmic amplifier simulation.