log amplifier and antilog amplifier
The BC547B and BC557B don't match perfectly in their b-e junction I-V characteristic. When I simulate driving equal current through the b-e of these two devices I see about 12 mV difference in the required b-e voltage:



(vp being the voltage applied to the BC557's junction and -vn being the voltage applied to the BC547's b-e junction to achieve equal current)

This difference will result in more current flowing through Q3 than the sum of currents through Q2 and Q1, and the output of your circuit being greater than the product of the values of the two input voltages. You can check this in your simulation by plotting the emitter currents of the three transistors.

If you find a way to use BC547 for the antilog function, this circuit ought to work in simulation. But in real life, you'll find that device-to-device variations (and thermal differences between the different transistors) will still result in some error in the output voltage, relative to the nominal multiplying behavior.