AHSME 1973 Problem 28

If $a$, $b$, and $c$ are in geometric progression (G.P.) with $1 1$ is an integer, then $\log_an$, $\log_bn$, $\log_cn$ form a sequence $\textbf{(A)}\ \text{which is a G.P}$ $\textbf{(B)}\ \text{which is an arithmetic progression (A.P)}$ $\textbf{(C)}\ \text{in which the reciprocals of the terms form an A.P}$ $\textbf{(D)}\ \text{in which the second and third terms are the }n\text{th powers of the first and second respectively}$ $\textbf{(E)}\ \text{none of these}$