Answer
See below.
Work Step by Step
We know that $\log_a1=0$ and that $\log_a x+\log_a y=log_a (x\cdot y)$, hence $\log_a{(x+\sqrt{x^2-1})}+\log_a{(x-\sqrt{x^2-1})}=\log_a{(x+\sqrt{x^2-1})(x-\sqrt{x^2-1})}=\log_a{(x^2-(x^2-1))}=\log_a{1}=0$
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding - Page 460: 101
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