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If 2^(x+3) = 32, what is the value of x?

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Question: If 2^(x+3) = 32, what is the value of x?

Options:

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

Correct Answer: 3

Solution: 

Since 32 can be expressed as 2^5, we have 2^(x+3) = 2^5, thus x + 3 = 5, leading to x = 2.

If 2^(x+3) = 32, what is the value of x?

Practice Questions

Q1
If 2^(x+3) = 32, what is the value of x?
  1. 1
  2. 2
  3. 3
  4. 5

Questions & Step-by-Step Solutions

If 2^(x+3) = 32, what is the value of x?
  • Step 1: Start with the equation 2^(x+3) = 32.
  • Step 2: Recognize that 32 can be written as a power of 2. Specifically, 32 = 2^5.
  • Step 3: Rewrite the equation using this information: 2^(x+3) = 2^5.
  • Step 4: Since the bases (2) are the same, we can set the exponents equal to each other: x + 3 = 5.
  • Step 5: Solve for x by subtracting 3 from both sides: x = 5 - 3.
  • Step 6: Calculate the result: x = 2.
  • Exponential Equations – The question tests the ability to solve equations involving exponents by equating the bases.
  • Logarithmic Understanding – Understanding how to manipulate and solve for variables in exponential forms.
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