Question

Log a, logb, and log c will be in which of the following series if it is given that a, b and c are in g.p

Answer 1

refer this one . I have just taken the general terms of GP .

Answer 2

Answer:

㏒ a, ㏒ b, ㏒ c are in A.P  

Step-by-step explanation:

Given Problem

㏒ a, ㏒ b, and ㏒ c will be in which of the following series if it is given that a, b and c are in G.P  

⇒ a, b, c are in G.P  

⇒  $\frac{b}{a} = \frac{c}{b}$             [ ∵ the common ratio is equal in G.P ]

⇒ b² = ac  

          apply ㏒ on both sides

⇒  ㏒ b² = ㏒ ac  

⇒  2 ㏒ b = ㏒ a +  ㏒ c  

⇒  ㏒ b + ㏒ b = ㏒ a + ㏒ c

⇒  ㏒ b - ㏒ a = ㏒ c - ㏒ b          [ ∴ common difference is equal ]

             ㏒ a, ㏒ b, ㏒ c are in A.P