Question
Question: If log 2, log (2<sup>x</sup> – 1), log (2<sup>x</sup> + 3) are in A.P. Then x is equal to...
If log 2, log (2x – 1), log (2x + 3) are in A.P. Then x is equal to
A
25
B
log2 5
C
log3 2
D
log53
Answer
log2 5
Explanation
Solution
If ,
, logmc are in an A.P then
b2 = ac, so log 2, log (2x – 1), log (2x + 3) are in an A.P. then
(2x – 1)2 = 2.(2x + 3)
put 2x = t
̃ t2 – 4t – 5 = 0
̃ (t – 5) (t + 1) = 0
̃ t = 5 ( t ¹ – 1)
̃ 2x = 5 then x = log25