The number of solutions of the equation log 4 x - 1 = log 2 x - 3 is ______.

Step-by-step solution

log 4 x - 1 = log 2 x - 3 ⇒ 1 2 log 2 x - 1 = log 2 x - 3 ⇒ log 2 x - 1 1 / 2 = log 2 x - 3 ⇒ x - 1 1 / 2 = x - 3 ⇒ x - 1 = x 2 + 9 - 6 x ⇒ x 2 - 7 x + 10 = 0 ⇒ x - 2 x - 5 = 0 ⇒ x = 2 , 5 But x ≠ 2 because it is not satisfying the domain of given equation i.e log 2 x - 3 → its domain x > 3 finally x is 5 ∴ No. of solutions = 1 .