Question

Solve :  4^{x - 2} - 2^{x + 1} = 0

Answer 1

4^{x - 2} - 2^{x + 1} = 0
⇒ 4^{x - 2} = 2^{x + 1}
⇒ (2²)^{x - 2}  = 2^{x + 1}
⇒ 2^{2x - 4}  = 2^{x + 1}
We know that if bases are equal, the powers are equal
⇒ 2x - 4 = x + 1
⇒ 2x - x = 4 + 1
⇒ x = 5.