Discussion
If a = \(b^{x}\), b = \(c^{y}\) and c = \(a^{z}\), then the value of xyz is equal to :
Answer: C
The value of xyz is 1.
Substitute each relation into the one before it so that everything is expressed as a power of a.
\[ \begin{aligned} a &= b^{x} = (c^{y})^{x} = c^{xy} \\ &= (a^{z})^{xy} = a^{xyz} \end{aligned} \]
Since \(a = a^{1}\), the exponents must match, so xyz = 1 (for a base other than 0 or 1, the usual assumption in such questions).
−1 would give \(a = 1/a\), and 0 would give a = 1 for every a. abc is a product of the bases, not of the exponents, so it is not what the relations determine.
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