If `log_a a. log_c a +log_c b. log_a b + log_a c. log_b c=3 `(where `a, b, c` are different positive real nu then find the value of `a bc.`

Explanation

`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`