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If 10^(x) = 1000, what is the value of x? (2023)

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Question: If 10^(x) = 1000, what is the value of x? (2023)

Options:

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

Correct Answer: 3

Exam Year: 2023

Solution: 

Since 1000 can be expressed as 10^3, we have 10^x = 10^3, thus x = 3.

If 10^(x) = 1000, what is the value of x? (2023)

Practice Questions

Q1
If 10^(x) = 1000, what is the value of x? (2023)
  1. 2
  2. 3
  3. 4
  4. 1

Questions & Step-by-Step Solutions

If 10^(x) = 1000, what is the value of x? (2023)
  • Step 1: Start with the equation 10^(x) = 1000.
  • Step 2: Recognize that 1000 can be rewritten as a power of 10. Specifically, 1000 = 10^3.
  • Step 3: Now, rewrite the equation using this new information: 10^(x) = 10^3.
  • Step 4: Since the bases (10) are the same on both sides of the equation, we can set the exponents equal to each other: x = 3.
  • Step 5: Therefore, the value of x is 3.
  • 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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