ACFT ON VISUAL APCH TO SLC WAS LATE IN CONTACTING TWR FOR CLRNC.

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INBOUND ON VECTORS FOR VISUAL APCH TO RWY 35 KSLC; APCH CTL REQUESTED I MAINTAIN MAX FORWARD SPD; WHICH I COMPLIED WITH AND ACKNOWLEDGED. ABEAM THE APCH END OF RWY 35 ON L DOWNWIND; I WAS CLRED FROM 7000 TO 6500 FT (APPROX 2300 FT AGL); INSTRUCTED TO TURN L BASE AT APPROX 4 MI FROM THE APCH END OF RWY 35; FOLLOWED BY CLRNC FOR A VISUAL APCH. I WAS PREOCCUPIED WITH SHOWING MY AIRPLANE TO FLAP/GEAR SPD; WHICH I WOULD HAVE DONE SOONER HAD I KNOWN APCH WAS GOING TO TURN ME IN SO SOON. ALSO; THE ARPT WAS EXTREMELY BUSY THAT NIGHT AND APCH TURNED ME IN WHAT SEEMED VERY CLOSE TO A PROCEEDING ACFT. I WAS NOT INSTRUCTED TO CONTACT TWR. BY SHORT FINAL; THE PRECEDING ACFT HAD EXITED THE RWY. I HAD MY GEAR AND FLAPS DOWN AND PRELNDG CHKLIST/FLOW CHK COMPLETE WHEN I REALIZED I HADN'T RECEIVED LNDG CLRNC. I QUERIED APCH. HE REPLIED WITH 'CONTACT TWR' (NOT STATING FREQ); AND I CONTACTED TWR ON 118.3 AND RECEIVED CLRNC JUST BEFORE TOUCHING DOWN. AFTER CLRING THE RWY; GND CTL GAVE ME A NUMBER TO CONTACT TWR AFTER SHUTDOWN. AFTER SHUTDOWN; I CALLED TWR AND THE CTLR I SPOKE WITH SAID HE WANTED TO BE SURE I KNEW I WAS CLRED TO LAND PRIOR TO TOUCHDOWN; THAT PRIOR TO MY CALL-UP ON TWR FREQ; THE TWR HAD BEEN DISPLAYING A GREEN LIGHT GUN SIGNAL. WE DISCUSSED HOW IF APCH DOESN'T HAND ME OFF TO TWR WITHIN 5 MI OF THE RWY; I SHOULD BE EXTRA VIGILANT AND QUERY APCH MUCH SOONER. I WILL BE ALERT FOR THIS IN THE FUTURE; AND I'M SURE I WOULD HAVE CAUGHT THE MISTAKE SOONER; HAD I NOT BEEN SO HIGH ON APCH; FAST; AND CLOSE TO THE PRECEDING ACFT. ALSO; THE RTE IS NEW TO ME; AS WELL AS OPS AT KSLC.