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If 3^(2x) = 81, what is the value of x?

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Question: If 3^(2x) = 81, what is the value of x?

Options:

  1. 2
  2. 3
  3. 4
  4. 1

Correct Answer: 2

Solution: 

Since 81 = 3^4, we have 3^(2x) = 3^4, thus 2x = 4, giving x = 2.

If 3^(2x) = 81, what is the value of x?

Practice Questions

Q1
If 3^(2x) = 81, what is the value of x?
  1. 2
  2. 3
  3. 4
  4. 1

Questions & Step-by-Step Solutions

If 3^(2x) = 81, what is the value of x?
  • Step 1: Start with the equation 3^(2x) = 81.
  • Step 2: Recognize that 81 can be written as a power of 3. Specifically, 81 = 3^4.
  • Step 3: Rewrite the equation using this information: 3^(2x) = 3^4.
  • Step 4: Since the bases (3) are the same, we can set the exponents equal to each other: 2x = 4.
  • Step 5: Solve for x by dividing both sides of the equation by 2: x = 4 / 2.
  • Step 6: Simplify the right side: x = 2.
  • Exponential Equations – The question tests the ability to solve equations involving exponents by equating the bases.
  • Base Conversion – It requires recognizing that 81 can be expressed as a power of 3.
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