Resistor on pin 3 of a Log Amplifier
There is some thumb role in Selecting Resistor for a Grounded input pin of an op-amp :

Since an op-amp is not ideal, then current consumption of input pins will not be neglected. Then beside its high-impedance input of a op-amp, when you attach high value resistors to these input pins, sometimes input current of op-amp pin would be comparable with these resistor currents in feed back loops. In this situation considering op-amp as an ideal device is a long wrong assumption. 

Then first rule: choose your op-amp and resistor values in such a way that op-amp input current be far smaller than 1/10 of resistor currents on feedback loops.

The Second rule: as input current of op-amp input pins is not exactly zero, we choose R2 (according to your schematic index) equal to equivalent impedance that is seen from Vin- of op-amp . for example if we assume Rpi of transistor 2.5KR then equivalent impedance is 2.5K || 100K . This technique gives a approximate value for R2 according to mentioned reasons.