If \[\mathbf{x=}\frac{\sqrt{\mathbf{8}}\mathbf{+}\sqrt{\mathbf{2}}}{\mathbf{2}}\] and \[\mathbf{y=}\frac{\sqrt{\mathbf{8}}-\sqrt{\mathbf{2}}}{\mathbf{2}}\] then the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{121}}}\], \[\mathbf{(}{{\mathbf{x}}_{\mathbf{2}}}\mathbf{+4xy+}{{\mathbf{y}}_{\mathbf{2}}}\mathbf{)}\], equal to __________

• A. 1                                                         
• B. \[\frac{1}{2}\]    
• C. \[\frac{13}{4}\]                                                 
• D. 2
• E. None of these