Question

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if a1 , a2 , a3 are in G P then of positive terms then log a1 , log a2 loga3 is in

i) HP

ii) AP

iii) GP

iv) None of these

No SpaM ❎❎❎❎❎❎❎❎

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Answer 1

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Answer is AP

and the same case is vice versa

a2/ a1 = a3/ a1

(common ratio in GP)

taking log both side

log(a2/a1) = log ( a3/a2)

loga2 - log a1 = log a3 - loga2

so the difference is a so it is in AP

Thanks

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Answer 2

Answer:

ii) AP

Step-by-step explanation:

a₁ ,  a₂ ,  a₃  in GP

=> a₂ / a₁  =  a₃ / a₂      [ the common ratio ]

=> log ( a₂ / a₁ )  = log ( a₃ / a₂ )

=> log a₂  -  log a₁  =  log a₃  -  log a₂       [ a common difference ]

=> log a₁ ,  log a₂ ,  log a₃  are in AP