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What is `log(a+sqrt(a^(2)+1))+log((1)/(a+sqrt(a^(2)+1)))` equal to?

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What is
`log(a+sqrt(a^(2)+1))+log((1)/(a+sqrt(a^(2)+1)))` equal to?
A. 1
B. 0
C. 2
D. `(1)/(2)`
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1 Answer

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Correct Answer - B
Let `log(a+sqrt(a^(2)+1))+log((1)/(a+sqrt(a^(2)+1)))`
`=log(a+sqrt(a^(2)+1))+log1-log(a+sqrt(a^(2)+1))`
`=log(a+sqrt(a^(2)+1))-log(a+sqrt(a^(2)+1))`
`=0`
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