Q2 of 104 Page 468

If a, b, c are in GP, then show that log an, log bn, log cn are in AP.

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


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