- Evaluate the following powers of 3:
- \(3^{-2}=\)
- \(3^{-1}=\)
- \(3^0=\)
- \(3^1=3\)
- \(3^2=\)
- \(3^3=\)
- \(3^4=\)
Given \(3^x=3^5\) , what value of \(x\) makes the statement true?
Since the bases are equal \((3)\), for the statement to be true, then the exponents must also be equal. Therefore:
when the bases are the same, the exponents can be set equal to each other, and
\(x=5\) since \(3^5=3^5\)
For the equations shown in the table below, rewrite the equation so that the bases are the same on each side of the equation. Then, solve the equation for \(x\).
| # | Original Equation | Rewritten Equation | Solve for \(x\) |
| Example | \(3^x=27\) | \(3^x=3^3\) | \(x=3\) |
| 2. | \(3^x=\dfrac19\) | ||
| 3. | \(3^x=243\) | ||
| 4. | \(3^x=1\) | ||
| 5. | \(3^{-x}=81\) | ||
| 6. | \(3^{2x}=9^4\) |
