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If 2^(x+1) = 16, what is the value of x?

Practice Questions

Q1
If 2^(x+1) = 16, what is the value of x?
  1. 2
  2. 3
  3. 4
  4. 5

Questions & Step-by-Step Solutions

If 2^(x+1) = 16, what is the value of x?
  • Step 1: Start with the equation 2^(x+1) = 16.
  • Step 2: Recognize that 16 can be written as a power of 2. Specifically, 16 = 2^4.
  • Step 3: Now, rewrite the equation using this information: 2^(x+1) = 2^4.
  • Step 4: Since the bases (2) are the same, we can set the exponents equal to each other: x + 1 = 4.
  • Step 5: Solve for x by subtracting 1 from both sides: x = 4 - 1.
  • Step 6: Simplify the equation: x = 3.
  • Exponential Equations – The question tests the ability to solve equations involving exponents and to recognize equivalent forms of numbers.
  • Logarithmic Understanding – Understanding that if the bases are the same, the exponents can be set equal to each other.
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