CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
If log₃ 5 = a, then log₉ 25 expressed in terms of a is:
log₉ 25 equals a. By change of base, log₉ 25 = log₃ 25 divided by log₃ 9, which is 2a divided by 2. The factor 2 from the power in 25 cancels the factor 2 from the base 9 = 3².
- AaCorrect
- B2a
- Ca/2
- Da²
Explanation
log₉ 25 = log₃ 25 / log₃ 9 = 2 log₃ 5 / 2 = a. A common error is to take 2a by ignoring that the base 9 also squares 3.
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