CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
If log₂ 3 = p and log₃ 5 = q, then log₂ 15 in terms of p and q is:
log₂ 15 equals p + pq. Split 15 as 3 × 5 to get log₂ 3 + log₂ 5. Using the chain rule, log₂ 5 = log₂ 3 × log₃ 5 = pq. Adding gives p + pq.
- Ap + q
- Bp + pqCorrect
- Cpq
- Dp + q + pq
Explanation
log₂ 15 = log₂ 3 + log₂ 5. Now log₂ 5 = log₂ 3 × log₃ 5 = pq by chain rule of change of base. So log₂ 15 = p + pq. Option p + q wrongly treats log₂ 5 as q.
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