MCQ practice · SSC General Mathematics Board questions · Chapter 4: Exponents and Logarithms
Under what condition does aˣ = aʸ imply x = y?
Think it through first, then pick an option.
- a a < 0, a ≠ 1
- b a > 0, y < 1
- c a > 0, x > 1
- d a > 0, a ≠ 1
Answer and explanation
Correct answer: d a > 0, a ≠ 1
If a = 1 every index gives 1, so a ≠ 1 is needed; negative bases are excluded.
Why the other options are wrong
- a a < 0, a ≠ 1: The base must be positive, not negative.
- b a > 0, y < 1: The condition is on the base, not on the index y.
- c a > 0, x > 1: The condition is on the base; x > 1 is not required.
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