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In a certain context, if the expression 5^(x+1) = 125 is true, what is the value

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Question: In a certain context, if the expression 5^(x+1) = 125 is true, what is the value of x?

Options:

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Correct Answer: 2

Solution: 

Since 125 can be expressed as 5^3, we have 5^(x+1) = 5^3, thus x + 1 = 3, leading to x = 2.

In a certain context, if the expression 5^(x+1) = 125 is true, what is the value

Practice Questions

Q1
In a certain context, if the expression 5^(x+1) = 125 is true, what is the value of x?
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Questions & Step-by-Step Solutions

In a certain context, if the expression 5^(x+1) = 125 is true, 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: Replace 125 in the equation with 5^3. Now the equation is 5^(x+1) = 5^3.
  • Step 4: Since the bases (5) are the same, we can set the exponents equal to each other. This gives us x + 1 = 3.
  • Step 5: Solve for x by subtracting 1 from both sides of the equation: x = 3 - 1.
  • Step 6: Simplify the equation to find x = 2.
  • Exponential Equations – Understanding how to manipulate and solve equations involving exponents.
  • Base Conversion – Recognizing that numbers can be expressed as powers of a common base.
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