Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
146 views
in Algebra by (101k points)
closed by
The domain of function log (log sin(x)) is
1. 0 < x < π
2. 2nπ < x < (2n + 1)π, for n in N
3. Empty set
4. None of the above

1 Answer

0 votes
by (108k points)
selected by
 
Best answer
Correct Answer - Option 3 : Empty set

General points:

  • sin(x) is the function having a range between -1 and +1.
  • Log(x) is defined only when x is positive and greater than zero.


log (sin(x)) is defined only when 0 < sin(x) ≤ 1, and then range will be (−∞,0]

So, log [log (sin(x))] is undefined as the logarithm of non-positive numbers isn’t defined for real numbers.

Hence, Domain of log [ log (sin(x))]: ∅ (empty set)

Also, Range of log [log (sin(x))]: ∅ (empty set)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...