question_answer

If \[{{\mathbf{a}}^{\mathbf{6}}}=\text{ }{{\mathbf{b}}^{\mathbf{6}}}+{{\mathbf{c}}^{\mathbf{6}}}\], then the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{c}}}({{\mathbf{a}}^{\mathbf{2}}}-{{\mathbf{b}}^{\mathbf{2}}})+\mathbf{lo}{{\mathbf{g}}_{\mathbf{c}}}({{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}+\mathbf{ab})\]\[+\text{ }\mathbf{lo}{{\mathbf{g}}_{\mathbf{c}}}\left( {{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}+\mathbf{ab} \right)\] is equal to ________

A) 1                                                         

B) 3           

C) 6           

D) 0

E) None of these