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If a, b, c are in GP then log a 10 ,log b 10 and log b 10 are in a) AP b) GP c) HP d) none

If a, b, c are in GP then loga10 ,logb10 and logb10 are in 
a) AP b) GP c) HP d) none

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

Consider a,b,c as 10,100,1000

Take 1/loga, 1/log b, 1/log c

It will be 1/1, 1/2,1/3

The answer is HP

Regards
Spandan Patil
31 Points
4 years ago
Hello,
a, b, c are in G.P. so b2=ac.
 
Now the sequence whose type is to be found can be written as 1/log(a), 1/log(b), 1/log(c). We know that log(a), log(b), log(c) are in A.P as b2=ac (loga +logc = logac) Therefore sequence is in H.P. as the inverses of all elements were in A.P.

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