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If the bases on both sides of an equation are equal (and non-trivial), then:
ATheir powers can be equated
BThe bases must be re-divided
CTheir powers must be reciprocals
DNo conclusion can be drawn
Answer & Solution
Correct answer: A. Their powers can be equated
1. From the comparison rule of indices: if a^x = a^y (with a ≠ 0, 1), then x = y.
2. Equal bases on both sides allow direct equating of the exponents.
3. Example: 2^2 = 2^x implies x = 2.
_Source: ICMAI BoS CMA Foundation Paper 3 (Business Mathematics & Statistics), Module 2 §2.2 (Indices and Logarithms) + Module 5 (Standard Deviation), p. 112-160 + 318-340_