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If 5^(x+1) = 125, what is the value of x?

Practice Questions

Q1
If 5^(x+1) = 125, what is the value of x?
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Questions & Step-by-Step Solutions

If 5^(x+1) = 125, what is the value of x?
  • Step 1: Start with the equation 5^(x+1) = 125.
  • Step 2: Recognize that 125 can be rewritten as a power of 5. Specifically, 125 = 5^3.
  • Step 3: Now, rewrite the equation using this information: 5^(x+1) = 5^3.
  • Step 4: Since the bases (5) are the same, we can set the exponents equal to each other: x + 1 = 3.
  • Step 5: Solve for x by subtracting 1 from both sides: x = 3 - 1.
  • Step 6: Simplify the equation: x = 2.
  • Exponential Equations – The question tests the ability to solve equations involving exponents by recognizing equivalent forms.
  • Base Conversion – It requires converting a number (125) into a power of the same base (5) to facilitate solving for x.
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