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The sum of all (positive) solutions of the equation
log16x+logx16=log512x+logx512\log_{16}x +\log _x 16=\log_{512} x + \log_x {512}log16x+logx16=log512x+logx512
can be written as ab \frac{a}{b} ba, where aaa and bbb are coprime positive integers. What are the last three digits of a+ba+ba+b?
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