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If 2^(x-2) = 1/8, what is the value of x?

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Question: If 2^(x-2) = 1/8, what is the value of x?

Options:

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  2. 1
  3. 2
  4. 3

Correct Answer: 3

Solution: 

1/8 can be expressed as 2^-3. Therefore, 2^(x-2) = 2^-3 implies x - 2 = -3, so x = -1.

If 2^(x-2) = 1/8, what is the value of x?

Practice Questions

Q1
If 2^(x-2) = 1/8, what is the value of x?
  1. 0
  2. 1
  3. 2
  4. 3

Questions & Step-by-Step Solutions

If 2^(x-2) = 1/8, what is the value of x?
  • Step 1: Start with the equation 2^(x-2) = 1/8.
  • Step 2: Recognize that 1/8 can be rewritten as a power of 2. Since 1/8 = 2^-3, we can replace 1/8 in the equation.
  • Step 3: Now the equation looks like this: 2^(x-2) = 2^-3.
  • Step 4: Since the bases (2) are the same, we can set the exponents equal to each other: x - 2 = -3.
  • Step 5: Solve for x by adding 2 to both sides of the equation: x = -3 + 2.
  • Step 6: Simplify the right side: x = -1.
  • Exponential Equations – Understanding how to manipulate and solve equations involving exponents.
  • Properties of Exponents – Using the property that if the bases are the same, the exponents must be equal.
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