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If log_3(9) = x, what is the value of x?

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Question: If log_3(9) = x, what is the value of x?

Options:

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

Correct Answer: 2

Solution: 

log_3(9) = log_3(3^2) = 2.

If log_3(9) = x, what is the value of x?

Practice Questions

Q1
If log_3(9) = x, what is the value of x?
  1. 1
  2. 2
  3. 3
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Questions & Step-by-Step Solutions

If log_3(9) = x, what is the value of x?
Correct Answer: 2
  • Step 1: Understand that log_3(9) means 'to what power must 3 be raised to get 9?'.
  • Step 2: Recognize that 9 can be written as 3 raised to the power of 2, which is 3^2.
  • Step 3: Rewrite the equation: log_3(9) = log_3(3^2).
  • Step 4: Use the property of logarithms that says log_b(a^c) = c * log_b(a).
  • Step 5: Apply this property: log_3(3^2) = 2 * log_3(3).
  • Step 6: Know that log_3(3) equals 1 because 3 raised to the power of 1 is 3.
  • Step 7: Substitute back: 2 * log_3(3) = 2 * 1 = 2.
  • Step 8: Conclude that log_3(9) = 2, so x = 2.
  • Logarithmic Properties – Understanding how to manipulate logarithms, particularly using the property that log_b(a^c) = c * log_b(a).
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