Are you talking about the role of Q3 and Q4?Then subtracting two constant current biased Vbe is not remotely dividing it by 2, or taking a square root.
They neither divide it by two or take the square root.
The output of the detector is the mean of the sum of the squares at 3mV/dB scaling. (At Q3 emitter or Q4 emitter.)
Q4 provides a -Vbe level shift.
If the scale factor is defined as 6 mV/dB then the 3mV/dB mean of the sum of the squares is divided by two which is a log-domain square root of the mean of the sum of the squares.
Nothing electrically divides by two in the detector, certainly not Q3 or Q4.
A 3/6 change in scaling ratio divides it by two.
Q4 and associated components simply drop the final output by one Vbe. (And buffer the timing network.)
An actual THAT2252 has its log converter biased up by one Vbe at the noninverting input to offset itself from the absolute value current sinks.
(To give the rectifier current output compliance.)
The 2252's level shift then has a two Vbe offset to subtract: One from the log converter and one from the rectifier/log domain filter.
In the 2252 V2 = Vbe; V3 = 2Vbe.
See: http://www.proaudiodesignforum.com/imag ... ematic.JPG
The 2252 clone shown above has op amp A's non inverting input at ground.
It doesn't need to be biased up by one Vbe because the current rectifier ahead of it can work into a virtual ground.
Q4 (V3) only needs to offset one Vbe (Q3).
As a consequence, and to make the 2252 clone compatible with the THAT2252, only a single Vbe offset is required.
In the 2252 clone V2 = 0; V3 = Vbe.
There is no square root operation performed by Q3 or Q4.
If I look at the output with 3mV/dB scaling it's not giving me RMS.
If I use a 6mV/dB scale factor after the detector's output (either electrically or by definition) then a square root is performed on a 3mV/dB "mean of sum of squares" measurement and I get linear dB/log-scaled RMS readings.