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If 2^(2x) = 16, what is the value of x?

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Question: If 2^(2x) = 16, what is the value of x?

Options:

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  2. 2
  3. 3
  4. 4

Correct Answer: 2

Solution: 

16 can be expressed as 2^4. Therefore, 2^(2x) = 2^4 implies 2x = 4, so x = 2.

If 2^(2x) = 16, what is the value of x?

Practice Questions

Q1
If 2^(2x) = 16, what is the value of x?
  1. 1
  2. 2
  3. 3
  4. 4

Questions & Step-by-Step Solutions

If 2^(2x) = 16, what is the value of x?
  • Step 1: Start with the equation 2^(2x) = 16.
  • Step 2: Recognize that 16 can be written as a power of 2. Specifically, 16 = 2^4.
  • Step 3: Rewrite the equation using this information: 2^(2x) = 2^4.
  • Step 4: Since the bases (2) 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 – Understanding how to manipulate and solve equations involving exponents.
  • Base Conversion – Recognizing that numbers can be expressed as powers of a common base.
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