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If a, b, c are distinct positive real nu...

If `a, b, c` are distinct positive real numbers each different from unity such that `(log_b a.log_c a -log_a a) + (log_a b.log_c b-logb_ b) + (log_a c.log_b c - log_c c) = 0,` then prove that `abc = 1.`

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