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

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.