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Study guides › Level 8 · Algebra 2

Equations with x in the power

Level 8 · Algebra 2 · for questions like “2ˣ⁺¹ = 32. What is x?”

💡 The idea

If the same base is on both sides, the powers must be equal.

🪜 The steps

  1. Write the number as a power of the base: 32 = 2⁵.
  2. Make the powers equal: x + 1 = 5.
  3. Solve: x = 4.

✏️ Worked examples

1. 2ˣ⁺¹ = 32: 32 = 2⁵, so x + 1 = 5 and x = 4.

2. 3²ˣ = 81: 81 = 3⁴, so 2x = 4 and x = 2.

⚠️ Watch out

🎯 Try these

  1. 5ˣ = 125
  2. 2ˣ⁺³ = 64
  3. 3²ˣ = 729

Answers: 1) 3 2) 3 3) 3

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