Answer
See below.
Work Step by Step
$log_a(\sqrt x+\sqrt {x-1})+log_a(\sqrt x-\sqrt {x-1})=log_a(\sqrt x+\sqrt {x-1})(\sqrt x-\sqrt {x-1})=log_a((\sqrt x)^2-(\sqrt {x-1})^2)=log_a1=0$
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