What is the value of \[{{\left[ \mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\left( \mathbf{5 lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{100} \right) \right]}^{\mathbf{2}}}_{\mathbf{b}}\]

• A.  4                    
• B.  3             
• C.  2                                
• D.  1