If log(P) = (1/2)log(Q) = (1/3)log(R), then which of the following options is TRUE?

A. P^2 = Q^(1/2)R^2
B. Q^2 = PR
C. ...

Question

If log(P) = (1/2)log(Q) = (1/3)log(R), then which of the following options is TRUE?

A. P^2 = Q^(1/2)R^2
B. Q^2 = PR
C. Q^2 = R^2P^2
D. R = P^(1/2)Q^2

Accepted Answer

Q^2 = PR is always true when log(P) = (1/2)log(Q) = (1/3)log(R). Answer: B. All three log expressions are equal to some constant k. Setting log(P) = k, (1/2)log(Q) = k, and (1/3)log(R) = k lets us express P, Q, R in terms of a common base. Once we write P = 10^k, Q = 10^(2k), R = 10^(3k), we can verify algebraic relationships between them.

If log(P) = (1/2)log(Q) = (1/3)log(R), then which of the following options is TRUE? A. P^2 = Q^(1/2)R^2 B. Q^2 = PR C. Q^2 = R^2P^2 D. R = P^(1/2)Q^2