A B737-300 FLT LOSES BOTH VHF RADIOS AND USES THE LOST COM PROC IN THEIR APCH AND LNDG AT JAX; FL.

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DURING CLBOUT FROM BNA DURING A FREQ CHANGE WITH ZTL; THE #1 COM RADIO FAILED. WE SWITCHED TO THE #2 COM RADIO FOR COMS WITH ATC. I REQUESTED OFF FREQ AND CONTACTED BHM OPS AND ASKED THEY RELAY TO DAL OF OUR RADIO PROB SO THEY COULD BE PREPARED FOR FIXING THE PROB ON ARR AT JAX. THE #2 RADIO WORKED FINE UNTIL A FREQ CHANGE TO JAX APCH WHEN IT FAILED ALSO. WE WERE TOLD TO EXPECT THE ILS RWY 7 PRIOR. WE SQUAWKED 7700/7600 AND PROCEEDED TO THE FAF; PERFORMED A PROC TURN TO LOSE ALT; AND EXECUTED THE APCH. LNDG/APCH WAS UNEVENTFUL. AFTER CLRING THE RWY; THE #2 COM RADIO STARTED WORKING. WE TALKED TO GND CTL AND GOT A CLRNC TO THE GATE. I TALKED WITH GND CTL DURING THE TAXI IN AND THEY SAID NO CONFLICTS WERE HAD WITH OTHER TFC AND I CALLED ON THE PHONE TO THE TWR AFTERWARDS AND THEY STATED THE SAME; NO TFC PROBS WHATSOEVER. SUPPLEMENTAL INFO FROM ACN 510483: WE BOTH ATTEMPTED SEVERAL TIMES ON COM #1 RADIO TO CONTACT CTR; BUT NEITHER PLT WAS GOING OUT. CIRCUIT BREAKERS WERE CHKED AND NONE POPPED. WHEN I ATTEMPTED TO CHK IN WITH APCH CTL; WE NOTICED THAT THE COM #2 RADIO HAD GONE BAD TOO. WE ATTEMPTED TO MAKE CONTACT ON BOTH RADIOS WITH NO SUCCESS. IN THE DSCNT; WE MADE NOTE THAT ATC WAS CLRING OUR WAY FROM WHAT WE COULD SEE ON TCASII. FLEW THE FULL PROC TURN ILS RWY 7 TO A NON EVENTFUL FULL STOP. TWR WAS GIVING US THE GREEN LIGHT AND THE TRUCKS WERE WAITING. WE TAXIED CLR AND GAVE THE FIRE TRUCKS THE THUMBS UP.