Domain of truth

Algebra Level 5

We know that, \({\color{Green}{\log(xyz) =\log (x)+\log (y) + \log (z)}} \)

But it's not true for, \({\color{Red}{\log(xyz) = \log (x+y+z)}} \)

However, for some values of \(x,y\) and \(z\) the false property above is true.

If, \({-10\leq x,y,z\leq10}\) and \(x, y, z\) are integers, then find the total number of ordered triples \({(x,y,z)}\) for which the equation above is true.

Note: The domain of the \( \log \) function is positive reals.

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