Unable to generate AM wave using opamp log antiog multiplier
Your circuit idea might be flawed and I can't understand what your waveforms are in relationship to your circuit AND, your inputs into R4 and R5 don't appear to be sourced from anywhere so, start simple using the simplest form of AM circuit i.e. a diode like this: -



That will produce these waveforms: -



All the detail should be in the schematic above but, just in case: -


Carrier is 1 MHz sinewave 5 volt p-p superimposed on an offset of 2 volts DC
Modulation is 10 kHz 2.5 volt p-p with 1.25 volt DC offset
Output band-pass filter (L1 and C1) tuned to about 1 MHz.


I'm using a triangle wave modulation so that I can see it's fairly linear quite easily. Here's what sinewave modulation looks like: -



Start here and build on that. With a bit of circuit invention it can be made to be a full modulator with suppressed carrier if that is what you ultimately aim for.