I need to design this log amp to approximate the relationship: Vout = -3log(Vin/3Vref)
The example given uses: Vout = -log(Vin/Vout) and then states, because of the required behaviour Rref = Rin
I'm a bit lost on this circuit...Would my Rref = 1/3Rin?
Is gain set by the voltage divider R1 and R2?

 

Hi,

Is that LM109 really LM108?

I would recommend doing a simulation to find out unless you feel like doing some real transistor analysis using something similar to a spice model for the transistor. That's probably necessary because the circuit probably takes advantage of the log behavior of a diode or transistor. So you probably need the exponential model, and i am not sure if you want to go through all that calculation or not. If you try it in a simulator that may be good enough for your purpose.