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If (log)b a(log)c a+(log)a b(log)c b+(lo...

If `(log)_b a(log)_c a+(log)_a b(log)_c b+(log)_a c(log)_cc=3` (where `a , b , c` are different positive real numbers `!=1),` then find the value of `a b cdot`

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`log_(b)a*log_(c)a+log_(a)b*log_(c)b+log_(a)c*log_(b)c=3`
or `(loga)/(logb)(loga)/(logc)+(logb)/(loga)(logb)/(logc)+(logc)/(loga)(logc)/(logb)=3`
or `(loga)^(3)+(logb)^(3)+(logc)^(3)=3(loga)(logb)(logc)`
` or loga+logb+logc=0` (as a,b,c are different)
`rArr" "log abc = 0 or abc = 1`
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