CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
If a^x = b, b^y = c and c^z = a, where a, b, c are positive and not equal to 1, then the value of xyz is:
The value of xyz is 1. Substituting successively gives a = c^z = b^(yz) = a^(xyz). Because a is positive and not equal to 1, the exponents must be equal, so xyz equals 1.
- A0
- B1Correct
- C-1
- Dabc
Explanation
Substitute: a = c^z = (b^y)^z = b^(yz) = (a^x)^(yz) = a^(xyz). Since a ≠ 1 and a > 0, equating exponents gives xyz = 1. The value 0 would make a = 1, which is excluded.
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