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1973 AMC 12 Question 28

AMC12 · 1973 AMC 12

Question 28

If $a,$ $b,$ and $c$ are in geometric progression (G.P.) with $1\lt a\lt b\lt c$ and $n\gt1$ is an integer, then $\log_a n,$ $\log_b n,$ $\log_c n$ form a sequence
  1. which is a G.P.
  2. which is an arithmetic progression (A.P.)
  3. in which the reciprocals of the terms form an
    A.P.
  4. in which the second and third terms are the $n$th powers of
    the first and second respectively
  5. none of these