Question

if p,q,r are in gp then show that logp,logq,logr are in ap​

Answer 1

Since p, q and r are in GP,

b/a = c/b

=> b² = ac

logarithm on both sides,

=> log(b²) = log(ac)

=> 2log(b) = log(a) + log(c)

=> log(b) + log(b) = log(a) + log(c)

=> log(b) - log(a) = log(c) - log(b)

Since the difference between the consecutive terms is equal, these logarithms are in AP

Answer 2

Is it correct.......