Answer
See explanations.
Work Step by Step
Step 1. Use the formula $(a+b)(a-b)=a^2-b^2$, we have $(x+\sqrt {x^2-1})(x-\sqrt {x^2-1})=x^2-(x^2-1)=1$
Step 2. We have $log_a(x+\sqrt {x^2-1})+log_a(x-\sqrt {x^2-1})=log_a(x+\sqrt {x^2-1})(x-\sqrt {x^2-1})=log_a1=0$
