Question
Thu February 09, 2012 By: 10 Th A

If log 2, log(2^x-1) and log(2^x+3) are in A.P. ,then the value of x is ?

Expert Reply
Thu February 09, 2012
Since the terms are in AP
So , 2*log(2x - 1) = log2 + log(2x + 3)
 
log(2x - 1)2 = log(2(2x + 3))
 
Let 2x = t
 
So , (t-1)2 = 2(t+3)
t2 + 1 - 2t = 2t + 6
t2 - 4t - 5 = 0
(t -5)(t + 1) = 0
t = 5 , -1
But -1 is not as 2x cannot be -1 for any value of x
So 2x  = 5 ,
x = log25
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