- Evaluate the following powers of 3:
- \(3^{-2}=\dfrac{1}{9}\)
- \(3^{-1}=\dfrac{1}{3}\)
- \(3^0=1\)
- \(3^1=3\)
- \(3^2=9\)
- \(3^3=27\)
- \(3^4=81\)
| # | Original Equation | Rewritten Equation | Solve for \(x\) |
| Example | \(3^x=27\) | \(3^x=3^3\) | \(x=3\) |
| 2. | \(3^x=\dfrac19\) | \(3^x=3^{-2}\) | \(x=-2\) |
| 3. | \(3^x=243\) | \(3^x=3^5\) | \(x=5\) |
| 4. | \(3^x=1\) | \(3^x=3^0\) | \(x=0\) |
| 5. | \(3^{-x}=81\) | \(3^{-x}=3^4\) | \(-x=4; x=-4\) |
| 6. | \(3^{2x}=9^4\) | \(3^{2x}=(3^2)^4=3^8\) | \(2x=8; x=4\) |