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If 10^(x+2) = 1000, what is the value of x? (2023)

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Question: If 10^(x+2) = 1000, what is the value of x? (2023)

Options:

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Correct Answer: 1

Exam Year: 2023

Solution: 

Since 1000 can be expressed as 10^3, we have 10^(x+2) = 10^3, thus x + 2 = 3, leading to x = 1.

If 10^(x+2) = 1000, what is the value of x? (2023)

Practice Questions

Q1
If 10^(x+2) = 1000, what is the value of x? (2023)
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Questions & Step-by-Step Solutions

If 10^(x+2) = 1000, what is the value of x? (2023)
  • Step 1: Start with the equation 10^(x+2) = 1000.
  • Step 2: Recognize that 1000 can be rewritten as 10^3.
  • Step 3: Replace 1000 in the equation with 10^3, so now we have 10^(x+2) = 10^3.
  • Step 4: Since the bases (10) are the same, we can set the exponents equal to each other: x + 2 = 3.
  • Step 5: Solve for x by subtracting 2 from both sides: x = 3 - 2.
  • Step 6: Calculate the result: x = 1.
  • Exponential Equations – The question tests the ability to solve equations involving exponents by equating the bases.
  • Logarithmic Understanding – Understanding the relationship between exponential forms and their logarithmic counterparts is essential.
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