CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
If log₂ x = a, log₄ y = a, and x and y are positive, then y expressed in terms of x is:
From log₂ x = a, x equals 2 to the power a. From log₄ y = a, y equals 4 to the power a, which is 2 to the power 2a, that is x squared. So y = x².
- Ay = x²Correct
- By = x
- Cy = √x
- Dy = 2x
Explanation
x = 2^a. log₄ y = a gives y = 4^a = (2²)^a = 2^(2a) = (2^a)² = x². Choosing √x results from swapping the roles of x and y.
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