Answer : To prove: log an, log bn, log cn are in AP.

Given: a, b, c are in GP

Formula used: (i) log ab = log a + log b As a, b, c are in GP

⇒ b2 = ac

Taking power n on both sides

⇒ b2n = (ac)n

Taking log both side

⇒ logb2n = log(ac)n

⇒ logb2n = log(ancn)

⇒ 2logbn = log(an) + log(cn)

Whenever a,b,c are in AP then 2b = a+c, considering this and the above equation we can say that log an, log bn, log cn are in AP.

Hence Proved