Question

Solve for x:
2^2x+3 - 9 x 2^x + 1 = 0

Answer 1

2^2x+3 - 9 x 2^x + 1 = 0
2^2x . 2³ - 9 x 2^x + 1 = 0
Put2^x = t, so, 2^2x = t²
So, 2^2x . 2³ - 9 x 2^x + 1 = 0 becomes 8t² - 9t + 1 = 0
⇒ 8t² - 8t - t + 1 = 0
⇒ 8t(t - 1) - (t - 1) = 0
⇒ t - 1 = 0 or 8t - 1 = 0
⇒ t = 1 or t = `(1)/(8)`
⇒ 2^x = 1 or 2^x = `(1)/(2^3)`
⇒ 2^x = 2⁰ or 2^x = 2^-3
⇒ x = 0 or x = -3.