Question

If log2, log(2^x - 1) and log(2^x + 3) are in A.P., then x is equal to :

(A) 5/2 

(B) log₂5 

(C) log₃2 

(D) 3/2

Answer 1

Correct option (B)

Explanation:

log2, log(2^x –1), log(2^x + 3) → A.P.

(2^x –1)² = 2(2^x + 3) 

y² – 2y + 1 = 2y + 6 

y² – 4y – 5 = 0 

y = 5, – 1 

2^x = 5 

x = log₂5