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If log_2(x + 1) = 3, what is the value of x?

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Question: If log_2(x + 1) = 3, what is the value of x?

Options:

  1. 6
  2. 7
  3. 8
  4. 9

Correct Answer: 6

Solution: 

log_2(x + 1) = 3 implies x + 1 = 2^3 = 8 => x = 7.

If log_2(x + 1) = 3, what is the value of x?

Practice Questions

Q1
If log_2(x + 1) = 3, what is the value of x?
  1. 6
  2. 7
  3. 8
  4. 9

Questions & Step-by-Step Solutions

If log_2(x + 1) = 3, what is the value of x?
Correct Answer: 7
  • Step 1: Start with the equation log_2(x + 1) = 3.
  • Step 2: Understand that log_2 means 'to what power do we raise 2 to get (x + 1)?'.
  • Step 3: Since log_2(x + 1) = 3, we can rewrite this as 2 raised to the power of 3 equals (x + 1).
  • Step 4: Write the equation as 2^3 = x + 1.
  • Step 5: Calculate 2^3, which is 8. So now we have 8 = x + 1.
  • Step 6: To find x, subtract 1 from both sides of the equation: 8 - 1 = x.
  • Step 7: Calculate 8 - 1, which gives you x = 7.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to solve for the variable.
  • Exponential Functions – Recognizing the relationship between logarithms and exponents.
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