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If a,b,c are positive real numbers other...

If a,b,c are positive real numbers other than unity such that `[a(b+c-a)]/loga`=`[b(c+a-b)]/logb`=`[c(a+b-c)]/logc`,prove that `a^b.b^a`=`b^c.c^b`=`c^a.a^c`

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