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If 4^(x-1) = 1/16, what is the value of x? (2023)

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Question: If 4^(x-1) = 1/16, what is the value of x? (2023)

Options:

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Correct Answer: 2

Exam Year: 2023

Solution: 

Since 1/16 can be expressed as 4^(-2), we have 4^(x-1) = 4^(-2), thus x - 1 = -2, leading to x = -1.

If 4^(x-1) = 1/16, what is the value of x? (2023)

Practice Questions

Q1
If 4^(x-1) = 1/16, what is the value of x? (2023)
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  2. 1
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Questions & Step-by-Step Solutions

If 4^(x-1) = 1/16, what is the value of x? (2023)
  • Step 1: Start with the equation 4^(x-1) = 1/16.
  • Step 2: Recognize that 1/16 can be rewritten as a power of 4. Since 4^(-2) = 1/16, we can replace 1/16 with 4^(-2).
  • Step 3: Now the equation looks like this: 4^(x-1) = 4^(-2).
  • Step 4: Since the bases (4) are the same, we can set the exponents equal to each other: x - 1 = -2.
  • Step 5: Solve for x by adding 1 to both sides of the equation: x = -2 + 1.
  • Step 6: Simplify the right side: x = -1.
  • Exponential Equations – The question tests the ability to solve equations involving exponents by equating the bases.
  • Negative Exponents – Understanding how to manipulate negative exponents and their equivalent fractional forms is crucial.
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