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If 10^(2x) = 100, what is the value of x?

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Question: If 10^(2x) = 100, what is the value of x?

Options:

  1. 0
  2. 0.5
  3. 1
  4. 2

Correct Answer: 0.5

Solution: 

100 = 10^2, so 2x = 2, hence x = 1.

If 10^(2x) = 100, what is the value of x?

Practice Questions

Q1
If 10^(2x) = 100, what is the value of x?
  1. 0
  2. 0.5
  3. 1
  4. 2

Questions & Step-by-Step Solutions

If 10^(2x) = 100, what is the value of x?
  • Step 1: Start with the equation 10^(2x) = 100.
  • Step 2: Recognize that 100 can be rewritten as 10^2.
  • Step 3: Replace 100 in the equation with 10^2, so now the equation is 10^(2x) = 10^2.
  • Step 4: Since the bases (10) are the same, we can set the exponents equal to each other: 2x = 2.
  • Step 5: To solve for x, divide both sides of the equation by 2: x = 2 / 2.
  • Step 6: Simplify the right side: x = 1.
  • Exponential Equations – Understanding how to manipulate and solve equations involving exponents.
  • Logarithmic Relationships – Recognizing the relationship between exponents and logarithms, particularly in base 10.
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