CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
If log₁₀ x = a and log₁₀ y = b, then log₁₀ (x³ √y / 100) equals:
The expression equals 3a + b/2 − 2. The cube on x gives 3a, the square root of y gives half of b, and dividing by 100 subtracts log 100, which is 2.
- A3a + b/2 − 2Correct
- B3a + 2b − 2
- C3a + b/2 + 2
- Da³ + b/2 − 2
Explanation
log(x³)=3a, log(√y)=b/2, and log100=2 is subtracted because it is in the denominator. So the result is 3a + b/2 − 2. Adding 2 would wrongly treat division as multiplication.
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