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If a,b,c be three distinct positive numb...

If a,b,c be three distinct positive numbers, each different from 1 such that `("log"_ba"log"_ca-"log"_aa)+("log"_ab"log"_cb-"log"_b b)+("log"_ac"log"_bc-"log"_c c)=0`, then prove that abc=1

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