Find the value of x in the equation 2^(2x) + 4(2^x) – 32 = 0

Write 2^(2x) as (2^x)². Let u = 2^x. The equation becomes u² + 4u – 32 = 0.

Factorise: (u + 8)(u – 4) = 0, so u = -8 or u = 4.

2^x can never be negative, so u = 4. Then 2^x = 4 = 2², so x = 2. Check: 2⁴ + 4(2²) – 32 = 16 + 16 – 32 = 0.