CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
If log₅ 3 = a and log₃ 7 = b, then log₅ 7 equals:
log₅ 7 equals ab. By the change of base chain rule, log₅ 3 multiplied by log₃ 7 gives log 3/log 5 times log 7/log 3, and log 3 cancels, leaving log 7/log 5, that is log₅ 7.
- Aa + b
- Ba/b
- CabCorrect
- Db/a
Explanation
log₅ 7 = log₃ 7 × log₅ 3 by the chain rule: (log 7/log 3)(log 3/log 5) = log 7/log 5. So it equals ab. Adding the values (a + b) confuses the product rule of logs with the chain rule.
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