Domain of truth

Algebra Level 5

We know that, log(xyz)=log(x)+log(y)+log(z){\color{#20A900}{\log(xyz) =\log (x)+\log (y) + \log (z)}}

But it's not true for, log(xyz)=log(x+y+z){\color{#D61F06}{\log(xyz) = \log (x+y+z)}}

However, for some values of x,yx,y and zz the false property above is true.

If, 10x,y,z10{-10\leq x,y,z\leq10} and x,y,zx, y, z are integers, then find the total number of ordered triples (x,y,z){(x,y,z)} for which the equation above is true.

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

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