It is given that a, b and c are in G.P.
b2 = ac {using property of geometric mean}
(b2)n = (ac)n
b2n = an cn
Now, apply log on both the sides we get,
log b2n = log (an cn)
log (bn)2 = log an + log cn
2 log bn = log an + log cn
∴ log an, log bn, log cn are in A.P
