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![\[a^x=b\]](http://latex.artofproblemsolving.com/f/3/7/f375b04de3c53239b27b6d7abad77ded50419ae2.png)
![\[b^y=a\]](http://latex.artofproblemsolving.com/9/f/1/9f199df2a6672f2c121f76bbbbf16d857f7bcb3d.png)
![\[{a^x}^y=a\]](http://latex.artofproblemsolving.com/8/3/a/83a9dc65c79b012c6b82784abe87431cf6adf1c8.png)
![\[xy=1\]](http://latex.artofproblemsolving.com/4/9/7/4979305dd5b73b3790d6c4b89d10826fe6a6bbbc.png)
![\[\log_a b\log_b a=1\]](http://latex.artofproblemsolving.com/0/3/0/0307e46f37d6ad324959095283c8c5aa5f4de44a.png)
As a result, the answer should be 1 \boxed{A}.
