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> If $\log \_b a\cdot\log\_c a +\log \_a b\cdot\log\_c b+\log \_a c\cdot\log\_b c=3$ and $a,b,c$ are different positive real numbers not equal to 1, then find the value of $abc$. 
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I tried to simplify this by different methods like using the identity $\log\_b a=\frac{1}{\log\_a b}$, but I couldn't get anywhere. Addition, subraction can't be used. I am not able to figure out a way to simplify the LHS. It would be great if someone could help me to proceed with this problem.