If \({{\rm{x}}^{{\rm{In}}\left( {\frac{{\rm{y}}}{{\rm{z}}}} \right)}} \cdot {{\rm{y}}^{{\rm{In}}{{\left( {{\rm{xz}}} \right)}^2}}} \cdot {{\rm{z}}^{{\rm{In}}\left( {\frac{{\rm{x}}}{{\rm{y}}}} \right)}} = {{\rm{y}}^{4{\rm{\;In\;y}}}}\) for any x > 1, y > 1 and z > 1, then which one of the following is correct?
1
In y is the GM of In x, In x, In x and In z
2
In y is the AM of In x, In x, In x, In z
3
In y is the HM of In x, In x, In x and In z
4
In y is the AM of In x, In x, In z and In z