Wrong that is cubic equation
Let a,b,c be three distinct positive numbers which are in G.P.
If log_{c}a , log_{b}c , log_{a}b are in A.P., then the common difference of the A.P. is....
REPLY SOON.....

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log_{c}a + log_{a}b =2 log_{b}c
log a / log c + log b / log a = 2log c / log b
a
b = ar
c = ar^{2}
now proceed
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arey yaar ankit....main yeh sab kar chuka hoon....par answer nahin aa raha....it's a finite value....
THE ANSWER IS 3/2
that was a mistake which i posted earlier
log c / log b  log a / log c= diff..
log c= log a + 2 log r
log b = log a + log r
sub in 1 and reduce it... u hav to get it...but it is long i think so..
yeah it's long....can anyone give a shorter method.....becoz it's a multiple choice ques.....so required shorter method.....
yaar abhi tak kissi ne solution nahin diya.....what has happened to u tiitians.......
i ve got the answer
bt it s not at all a short approach
let a,b,c be A/r,A,Ar
let log_{A}r=t
i took all log to base b(or u cud say toA)
so wat s given is
2(1+t)=1/(1t)+(1t)/1+t
solving it we get
2t^{2}+3t3=0
2t^{2}=3(1t)
t^{2}/1t=3/2
as we ve to find the value of common difference
its = t^{2}/1t
so here is d ans ne short approach is invited [1]
hey richa i think there is some problem in ur solution i think u have taken...
log_{b}r=t....but u have written log_{a}r=t.....
plssss just check it out....
actually i think u get confused as i took variable same as a waitt i m editting