Question

Solve for x:
2^2x + 2^{x +2} - 4 x 2³ = 0

Answer 1

2^2x + 2^{x +2} - 4 x 2³ = 0
⇒ 2^2x + 2^x+2 - 2² x 2³ = 0
⇒ 2^2x + 2^x . 2² - 2²⁺³ = 0       ......(Using a^m x aⁿ = a^m+n)
⇒ 2^2x + 2^x . 2² - 2⁵ = 0
⇒ 2^2x + 2^x . 4 - 32 = 0
Put 2^x = t
So, 2^2x = t²
2^2x + 2^x+2 - 32 = 0 becomes t² + 4t - 32 = 0
⇒ (t + 8)(t - 4) = 0
⇒ t + 8 = 0 or t - 4 = 0
⇒ t = -8 = 0 or t = 4
⇒ 2^x = -8 or 2^x = 4
⇒ 2x = -2³ or 2^x = 2²
Using the second equation 2^x = 2², we get x = 2.