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If log_3(x + 1) = 2, what is the value of x?

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Question: If log_3(x + 1) = 2, what is the value of x?

Options:

  1. 2
  2. 8
  3. 3
  4. 5

Correct Answer: 8

Solution: 

log_3(x + 1) = 2 implies x + 1 = 3^2 = 9 => x = 8.

If log_3(x + 1) = 2, what is the value of x?

Practice Questions

Q1
If log_3(x + 1) = 2, what is the value of x?
  1. 2
  2. 8
  3. 3
  4. 5

Questions & Step-by-Step Solutions

If log_3(x + 1) = 2, what is the value of x?
Correct Answer: 8
  • Step 1: Start with the equation log_3(x + 1) = 2.
  • Step 2: Understand that log_3 means 'to what power must 3 be raised to get (x + 1)?'.
  • Step 3: Since log_3(x + 1) = 2, this means 3 raised to the power of 2 equals (x + 1).
  • Step 4: Write this as an equation: x + 1 = 3^2.
  • Step 5: Calculate 3^2, which is 9. So now we have x + 1 = 9.
  • Step 6: To find x, subtract 1 from both sides: x = 9 - 1.
  • Step 7: Calculate 9 - 1, which gives you x = 8.
  • 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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