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If 5^(x-1) = 25, what is the value of x?

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Question: If 5^(x-1) = 25, what is the value of x?

Options:

  1. 2
  2. 3
  3. 4
  4. 1

Correct Answer: 2

Solution: 

Since 25 = 5^2, we have 5^(x-1) = 5^2, thus x - 1 = 2, giving x = 3.

If 5^(x-1) = 25, what is the value of x?

Practice Questions

Q1
If 5^(x-1) = 25, what is the value of x?
  1. 2
  2. 3
  3. 4
  4. 1

Questions & Step-by-Step Solutions

If 5^(x-1) = 25, what is the value of x?
  • Step 1: Start with the equation 5^(x-1) = 25.
  • Step 2: Recognize that 25 can be rewritten as 5^2.
  • Step 3: Replace 25 in the equation with 5^2, so now we have 5^(x-1) = 5^2.
  • Step 4: Since the bases (5) 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: Therefore, x = 3.
  • Exponential Equations – The question tests the ability to solve equations involving exponents by equating the bases.
  • Base Conversion – It requires recognizing that 25 can be expressed as a power of 5.
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