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If log a, log b, and log c are in A.P. and also log a – log 2b, log 2b – log 3c, log 3c – log a are in A.P., then
- a)a, b, c, are in H.P.
- b)a, 2b, 3c are in A.P.
- c)a, b, c are the sides of a triangle
- d)none of the above
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If log a, log b, and log c are in A.P. and also log a – log 2b, ...
Given Information:
- log a, log b, and log c are in A.P.
- log a - log 2b, log 2b - log 3c, log 3c - log a are in A.P.
Explanation:
Using the given information:
- If log a, log b, and log c are in A.P., then we have: 2log b = log a + log c
- Similarly, from the second set of information, we have: 2log 2b = log 3c + log a
Converting the above equations:
- From the first equation, we get: log b = (log a + log c) / 2 = log √(ac)
- From the second equation, we get: log 2b = (log 3c + log a) / 2 = log √(3ac)
Therefore:
- We can write b = √(ac) and 2b = √(3ac)
- This implies a, b, and c are in A.P.
Conclusion:
- Hence, option c) a, b, c are the sides of a triangle is the correct answer.
- log a, log b, and log c are in A.P.
- log a - log 2b, log 2b - log 3c, log 3c - log a are in A.P.
Explanation:
Using the given information:
- If log a, log b, and log c are in A.P., then we have: 2log b = log a + log c
- Similarly, from the second set of information, we have: 2log 2b = log 3c + log a
Converting the above equations:
- From the first equation, we get: log b = (log a + log c) / 2 = log √(ac)
- From the second equation, we get: log 2b = (log 3c + log a) / 2 = log √(3ac)
Therefore:
- We can write b = √(ac) and 2b = √(3ac)
- This implies a, b, and c are in A.P.
Conclusion:
- Hence, option c) a, b, c are the sides of a triangle is the correct answer.
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If log a, log b, and log c are in A.P. and also log a – log 2b, log 2b – log 3c, log 3c – log a are in A.P., thena)a, b, c, are in H.P.b)a, 2b, 3c are in A.P.c)a, b, c are the sides of a triangled)none of the aboveCorrect answer is option 'C'. Can you explain this answer?
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If log a, log b, and log c are in A.P. and also log a – log 2b, log 2b – log 3c, log 3c – log a are in A.P., thena)a, b, c, are in H.P.b)a, 2b, 3c are in A.P.c)a, b, c are the sides of a triangled)none of the aboveCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If log a, log b, and log c are in A.P. and also log a – log 2b, log 2b – log 3c, log 3c – log a are in A.P., thena)a, b, c, are in H.P.b)a, 2b, 3c are in A.P.c)a, b, c are the sides of a triangled)none of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log a, log b, and log c are in A.P. and also log a – log 2b, log 2b – log 3c, log 3c – log a are in A.P., thena)a, b, c, are in H.P.b)a, 2b, 3c are in A.P.c)a, b, c are the sides of a triangled)none of the aboveCorrect answer is option 'C'. Can you explain this answer?.
If log a, log b, and log c are in A.P. and also log a – log 2b, log 2b – log 3c, log 3c – log a are in A.P., thena)a, b, c, are in H.P.b)a, 2b, 3c are in A.P.c)a, b, c are the sides of a triangled)none of the aboveCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If log a, log b, and log c are in A.P. and also log a – log 2b, log 2b – log 3c, log 3c – log a are in A.P., thena)a, b, c, are in H.P.b)a, 2b, 3c are in A.P.c)a, b, c are the sides of a triangled)none of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log a, log b, and log c are in A.P. and also log a – log 2b, log 2b – log 3c, log 3c – log a are in A.P., thena)a, b, c, are in H.P.b)a, 2b, 3c are in A.P.c)a, b, c are the sides of a triangled)none of the aboveCorrect answer is option 'C'. Can you explain this answer?.
Solutions for If log a, log b, and log c are in A.P. and also log a – log 2b, log 2b – log 3c, log 3c – log a are in A.P., thena)a, b, c, are in H.P.b)a, 2b, 3c are in A.P.c)a, b, c are the sides of a triangled)none of the aboveCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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