Q62.If sum of the first 21 terms of the series log91/2 x + log91/3 x + log91/4 x + … . . where x > 0 is 504, then x is equal to (1) 243 (2) 9 (3) 7 (4) 81
What This Question Tests
This question tests the understanding of logarithm properties and the ability to identify an arithmetic progression within a series of logarithmic terms. It requires simplification of each term using log rules and then summing the resulting AP.
Concepts Tested
Formulas Used
log_b (M^p) = p log_b M
log_b (M/N) = log_b M - log_b N
Sum of AP = n/2 * (2a + (n-1)d)
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Sum of series involving logarithms
- Year
- 2021
- Shift
- 20 Jul Shift 2
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series
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