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Given that (log P)/(y-z)=(log Q)/(z-x)=(log R)/(x-y)=10 for x ≠ y ≠ z, what is the value of the product PQR?
- 0
- 1
- xyz
- 10^xyz
Correct answer: 1
Solution
The equations imply that log P = 10(y-z), log Q = 10(z-x), and log R = 10(x-y). Adding these gives log P + log Q + log R = 10[(y-z) + (z-x) + (x-y)] = 10(0) = 0, which means log(PQR) = 0, leading to PQR = 10⁰ = 1.
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