If a, b, c are in G.P., prove that log a, log b, log c are in A.P.
If a, b, c are in GP
⇒ .....(i)
We know,
log a – log b = {property of logarithm}
and according to equation (i)
⇒
⇒ log b – log a = log c – log b
⇒ 2 log b = log a + log c {property of arithmetic mean}
Hence they are in AP. …proved