Study guides › Level 8 · Algebra 2

Equations with logs

Level 8 · Algebra 2 · for questions like “log₂ (x − 3) = 5. What is x?”

💡 The idea

log_b (something) = n means something = bⁿ. Rewriting it without the log solves it.

🪜 The steps

1. Rewrite: x − 3 = 2⁵.
2. Work out the power: 2⁵ = 32.
3. Solve: x = 35.

✏️ Worked examples

1. log₂ (x − 3) = 5: x − 3 = 32, so x = 35.

2. log₁₀ x = 3: x = 10³ = 1,000.

⚠️ Watch out

• Check your answer by putting it back in. The number inside a log must come out positive.

🎯 Try these

1. log₃ x = 4
2. log₅ (x − 10) = 2
3. log₂ (x + 1) = 6

Answers: 1) 81 2) 35 3) 63

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.