Question

Solve: 

2^2x + 2^x+2 − 4 × 2³ = 0

Answer 1

Given: 2^2x + 2^{x + 2} − 4 × 2³ = 0

2^(2x) + 2^(x).2⁽²⁾ − 4 × 8 = 0

Substituting 2^x = a, we get:

a² + 4a − 32 = 0

a² + 8a − 4a − 32 = 0

a(a + 8) − 4(a + 8) = 0

(a − 4)(a + 8) = 0

a − 4 = 0 or a + 8 = 0

a = 4 or a = −8

a cannot be negative as 2^x, for any value of x is greater than 0.

a = 4

2^x = 4

2^x = 2²

x = 2