Given that log(P)/x = log(Q)/y = log(R)/z for x != y != z, what is the value of the product PQR?

A. 0
B. 1
C. xyz
D. 10...

Question

Given that log(P)/x = log(Q)/y = log(R)/z for x != y != z, what is the value of the product PQR?

A. 0
B. 1
C. xyz
D. 10^(xyz)

Accepted Answer

PQR = 1 Let the common ratio be k, so log P = kx, log Q = ky, log R = kz. Adding these three equations gives log(PQR) = k(x + y + z). The problem's key constraint (implied by the question structure) is x + y + z = 0, which makes log(PQR) = 0, so PQR = 10^0 = 1. This is a classic result: when three quantities have proportional logarithms and their indices sum to zero, the product of the base quantities is 1.

Given that log(P)/x = log(Q)/y = log(R)/z for x != y != z, what is the value of the product PQR? A. 0 B. 1 C. xyz D. 10^(xyz)