I need to convert logarithmic forms to exponent forms. Let me work through each problem step by step.
The relationship between logarithmic and exponential form is:
- If log_b(a) = c, then b^c = a
Let me solve each one:
1. log₃ 9 = 2
- Base is 3, result is 9, exponent is 2
- Exponent form: 3² = 9
2. log₄ 64 = 3
- Base is 4, result is 64, exponent is 3
- Exponent form: 4³ = 64
3. log₅ 25 = 2
- Base is 5, result is 25, exponent is 2
- Exponent form: 5² = 25
4. log₂ 128 = 7
- Base is 2, result is 128, exponent is 7
- Exponent form: 2⁷ = 128
5. log₃(1/27) = -3
- Base is 3, result is 1/27, exponent is -3
- Exponent form: 3⁻³ = 1/27
6. log₆ 36 = 2
- Base is 6, result is 36, exponent is 2
- Exponent form: 6² = 36
7. log₅(1/625) = -4
- Base is 5, result is 1/625, exponent is -4
- Exponent form: 5⁻ = 1/625
Let me verify my answers:
- 3² = 9 ✓
- 4³ = 64 ✓
- 5² = 25 ✓
- 2⁷ = 128 ✓
- 3⁻³ = 1/3³ = 1/27 ✓
- 6² = 36 ✓
- 5⁻⁴ = 1/5⁴ = 1/625 ✓
All conversions are correct!
Final Answer:
| Logarithmic Form | Exponent Form |
|------------------|---------------|
| log₃ 9 = 2 | 3² = 9 |
| log₄ 64 = 3 | 4³ = 64 |
| log₅ 25 = 2 | 5² = 25 |
| log₂ 128 = 7 | 2⁷ = 128 |
| log₃(1/27) = -3 | 3⁻³ = 1/27 |
| log₆ 36 = 2 | 6² = 36 |
| log₅(1/625) = -4 | 5⁻⁴ = 1/625 |
Parent Tip: Review the logic above to help your child master the concept of exponents and logarithms worksheet.
