Vo = -nVt (ln (Vin/R1) - ln Io)
Vo - Output voltage
n - Intrinsic semiconductor rate
Vt - Thermal equivalent of voltage = 26mV
ln - log to base e
Vin - Input voltage
R1 - Input series resistance = 1Kohm
Io = leakage current of diode
Vo is proportional to ln (Vin/R1)
Output is proportional to logarithmic of input.
Therefore the name Logarithmic Amplifier