A STUDENT PLT FLYING A C340 ON SOLO MULTI-ENG XCOUNTRY TURNS TO THE WRONG HDG AFTER TKOF.

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ON NOV/XX/96; I DEPARTED SLC ON A SOLO FLT AS A STUDENT PLT FLYING A TWIN CESSNA 340A ACFT. I HAVE 465 HRS TOTAL TIME AS A STUDENT PLT; WITH OVER 300 HRS IN THIS PARTICULAR ACFT. THE ACFT IS BASED AT SLC AND IS OWNED BY A PVT COMPANY IN WHICH I AM THE PRINCIPAL OWNER. I HAVE MADE APPROX 170 DEPS FROM SLC FLYING THIS ACFT. AT THE TIME OF THIS INCIDENT; RWY 34R WAS CLOSED FOR REPAIRS. I WAS CLRED TO DEPART ON RWY 35; WHICH IS E OF RWY 34R. AFTER TKOF AND DURING INITIAL CLB; I WAS GIVEN AN INSTRUCTION BY SLC TWR FOR A L TURN. I SOMEHOW MISUNDERSTOOD THAT INSTRUCTION AND INTERPRETED THE INSTRUCTION TO BE FOR A L TURN TO THE APCH END OF RWY 16R; WHICH IS WELL TO THE W OF RWY 35. I LATER LISTENED TO THE TWR TAPE RECORDING AND LEARNED THAT THE ATC ACTUALLY GAVE ME AN INSTRUCTION TO FLY THE APCH END OF RWY 34L. I CONTINUED ON MY FLT UNAWARE OF ANY INCIDENT. I WAS GIVEN NO CORRECTIVE VECTOR HDG BY THE ATC AT ANYTIME AFTER TKOF; EVEN THOUGH BY MY ESTIMATE THE ELAPSED TIME FROM MY INITIAL L TURN UNTIL I REACHED THE APCH END OF RWY 16R WOULD HAVE BEEN ABOUT 1.3 MINS.