If 2ˣ = 32, find x.

**The reasoning** You need to ask yourself: "What power of 2 gives me 32?" Let's break down powers of 2: - 2¹ = 2 - 2² = 4 - 2³ = 8 - 2⁴ = 16 - 2⁵ = 32 ✓ So x = 5. **The principle:** When solving exponential equations like 2ˣ = 32, express both sides with the same base if possible. Here, 32 = 2⁵, so 2ˣ = 2⁵, which means x = 5. **Why the wrong options tempt you** - **Option A (2):** You might confuse the base with the exponent. Don't just look at the "2" in the question! - **Option B (3):** Comes from 2³ = 8. Students sometimes stop counting too early. - **Option C (4):** This gives 2⁴ = 16. Close, but not quite 32. A calculation slip. **Quick takeaway** When you see 2ˣ = (some number), mentally run through your multiplication table of 2s until you hit that number — that position is your x!