Solveeit Logo

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

52\frac { 5 } { 2 }

B

log2 5

C

log3 2

D

log53

Answer

log2 5

Explanation

Solution

If , , logmc\log _ { m } \mathrm { c } 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\log _ { 2 } 5