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?

In y is the HM of In x, In x, In x and In z

In y is the GM of In x, In x, In x and In z

In y is the AM of In x, In x, In x, In z

In y is the AM of In x, In x, In z and In z

If \({{\rm{x}}^{{\rm{In}}\left( {\frac{{\rm{y}}}{{\rm{z}}}} \right)}}

1.	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?
A.	In y is the GM of In x, In x, In x and In z
B.	In y is the AM of In x, In x, In x, In z
C.	In y is the HM of In x, In x, In x and In z
D.	In y is the AM of In x, In x, In z and In z
Answer» C. In y is the HM of In x, In x, In x and In z

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