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3 Answers

Best answer
12 votes
12 votes
log( log sin(x) )

-1 <= sinx<= +1

log a is defined for positive values of a,

log sin(x)  is defined for sin(x)= (0,1]

Possible values for  log sin(x) = ($-\infty$ , 0]

Domain of log( log sin(x) )=Not defined

Therefore, Answer (c) Empty Set
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1 votes
1 votes
Option C is correct.

We can satisfy inner log using $x=\pi / 2$, but can't satisfy outer log at the same time. Thus, empty set.
1 votes
1 votes
$\log sin(x)>0 => sin (x)>e^0.$

Now this is impossible because the value of sin cannot be greater than 1.

Therefore, empty set is the answer.
Answer:

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