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If 10^(x+2) = 1000, what is the value of x? (2023)
If 10^(x+2) = 1000, what is the value of x? (2023)
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If 10^(x+2) = 1000, what is the value of x? (2023)
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Since 1000 can be expressed as 10^3, we have 10^(x+2) = 10^3, thus x + 2 = 3, leading to x = 1.
Questions & Step-by-step Solutions
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Q: If 10^(x+2) = 1000, what is the value of x? (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.
Steps: 6
Show Steps
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.
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