CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
If log₂ x = a, log₄ y = a and x, y > 0, with a ≠ 0, then the relation between x and y is:
The correct relation is y = x². From log₂ x = a, x = 2^a; from log₄ y = a, y = 4^a = (2^a)² = x². For a = 1, x = 2 and y = 4, confirming y equals x squared.
- Ay = x²
- Bx = y²Correct
- Cx = y
- Dy = 2x
Explanation
x = 2^a. log₄ y = a gives y = 4^a = 2^(2a) = (2^a)² = x². So y = x², and option x = y² is the reverse mistake. Check with a = 1: x = 2, y = 4, y = x².
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