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If a, b, c are in G.P. and logc a, logb c, loga b are in A.P., then the common difference on the A.P. is

If a, b, c are in G.P. and logc a, logb c, loga b are in A.P., then the common difference on the A.P. is

Grade:12th pass

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
a, b, c are in GP => b2 = ac -------(1)
       Also log (ac) + log(ab) = 2log(bc)
  • Log(a2bc) = log (b2c2)
  • a2bc = b2c2
  • a2 = bc ------(2)
 
             from 1 and 2 , a=b
           
common difference of AP = log(ac/bc) = log(a/b) = log(1)
                                           = 0
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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