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If 5^(2x) = 25, what is the value of x?

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Question: If 5^(2x) = 25, what is the value of x?

Options:

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Correct Answer: 1

Solution: 

25 can be expressed as 5^2. Therefore, 5^(2x) = 5^2 implies 2x = 2, so x = 1.

If 5^(2x) = 25, what is the value of x?

Practice Questions

Q1
If 5^(2x) = 25, what is the value of x?
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Questions & Step-by-Step Solutions

If 5^(2x) = 25, what is the value of x?
  • Step 1: Start with the equation 5^(2x) = 25.
  • Step 2: Recognize that 25 can be rewritten as 5^2.
  • Step 3: Replace 25 in the equation with 5^2, so now we have 5^(2x) = 5^2.
  • Step 4: Since the bases (5) are the same, we can set the exponents equal to each other: 2x = 2.
  • Step 5: Solve for x by dividing both sides of the equation by 2: x = 2 / 2.
  • Step 6: Simplify the right side to find x = 1.
  • Exponential Equations – Understanding how to manipulate and solve equations involving exponents.
  • Base Matching – Recognizing that if the bases are the same, the exponents must be equal.
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