2\(^{\sqrt{2x + 1}}\) = 32

2\(^{\sqrt{2x + 1}}\) = 2\(^5\)

\(\sqrt{2x + 1}\) = 5

square both sides

2x + 1 = 5\(^2\)

2x + 1 = 25

2x = 25 - 1

2x = 24

x = \(\frac{24}{2}\)

x = 12