Solve: 2$^{\sqrt{2x + 1}}$ = 32

Analyze the question: We need to find x such that 2 raised to the power √(2x + 1) equals 32.

Concept: If the bases are the same, the exponents must be equal. So write 32 as a power of 2.

Solution:

1. Write 32 as a power of 2: 32 = 2⁵
2. Equate the exponents: √(2x + 1) = 5
3. Square both sides: 2x + 1 = 25
4. Solve: 2x = 24, so x = 12

Check: If x = 12, then 2x + 1 = 25, √25 = 5, and 2⁵ = 32. ✓

Answer: x = 12, which is option C.

Tip: For exponential equations, always rewrite both sides with the same base first (2, 3, 5 and their powers come up often). Memorize powers of 2 up to 2¹⁰: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. When a square root appears, square both sides, then check your answer in the original equation.