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CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms

If a^x = b, b^y = c and c^z = a, then the value of xyz is:

The value of xyz is 1. Substituting successively, a = c^z = (b^y)^z = b^(yz) = (a^x)^(yz) = a^(xyz). Equating the exponents of the same base a gives xyz = 1, valid when a is positive and not equal to 1.

  1. A0
  2. B1Correct
  3. Cabc
  4. D−1

Explanation

a = c^z = (b^y)^z = b^(yz) = (a^x)^(yz) = a^(xyz). So a^1 = a^(xyz), giving xyz = 1 (for a ≠ 1). The value abc is not a constant exponent relation.

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