Question 848902
log a, log b, log c are in arithmetic progression iff 2 log b = log a + log c <--> log (b^2) = log ac (by logarithmic properties) <--> b^2 = ac, since the log function is one-to-one.


Note that b^2 = ac holds iff a/b = b/c, which is the criterion for a geometric sequence. We are assuming all terms are positive (although the statement should hold if a,b,c are negative, except log a, etc. is complex).