CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
If log₁₀ x = 2.5 and log₁₀ y = 1.5, then log₁₀ (x²/√y) equals:
The value is 4.25. Using the power and quotient laws, log(x²/√y) = 2 log x − ½ log y. Substituting gives 2 × 2.5 − 0.5 × 1.5 = 5 − 0.75 = 4.25.
- A4.25Correct
- B3.75
- C5.75
- D3.25
Explanation
log(x²/√y) = 2 log x − ½ log y = 2(2.5) − ½(1.5) = 5 − 0.75 = 4.25. The value 3.25 comes from subtracting 1.5 instead of half of it; 5.75 comes from adding 0.75.
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