EXPS 1 | Lesson 4 | Try This! (Solving Equations with Powers of 3)

  1. 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 EquationRewritten EquationSolve 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.\(3^{2x}=9^4\)

Check your solutions here.


Go to Watch (Solving Same-Base Equations)

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