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If 4^(x-1) = 64, what is the value of x?

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Question: If 4^(x-1) = 64, what is the value of x?

Options:

  1. 3
  2. 4
  3. 5
  4. 6

Correct Answer: 4

Solution: 

Since 64 can be expressed as 4^3, we have 4^(x-1) = 4^3, thus x - 1 = 3, leading to x = 4.

If 4^(x-1) = 64, what is the value of x?

Practice Questions

Q1
If 4^(x-1) = 64, what is the value of x?
  1. 3
  2. 4
  3. 5
  4. 6

Questions & Step-by-Step Solutions

If 4^(x-1) = 64, what is the value of x?
  • Step 1: Start with the equation 4^(x-1) = 64.
  • Step 2: Recognize that 64 can be rewritten as a power of 4. Specifically, 64 = 4^3.
  • Step 3: Now rewrite the equation using this information: 4^(x-1) = 4^3.
  • Step 4: Since the bases (4) are the same, we can set the exponents equal to each other: x - 1 = 3.
  • Step 5: Solve for x by adding 1 to both sides of the equation: x = 3 + 1.
  • Step 6: Therefore, x = 4.
  • Exponential Equations – The question tests the ability to solve equations involving exponents by equating the bases.
  • Base Conversion – It requires recognizing that 64 can be expressed as a power of 4, which is essential for solving the equation.
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