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What is the value of log_3(81)?

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Question: What is the value of log_3(81)?

Options:

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

Correct Answer: 4

Solution: 

log_3(81) = log_3(3^4) = 4.

What is the value of log_3(81)?

Practice Questions

Q1
What is the value of log_3(81)?
  1. 2
  2. 3
  3. 4
  4. 5

Questions & Step-by-Step Solutions

What is the value of log_3(81)?
Correct Answer: 4
  • Step 1: Understand that log_3(81) means 'to what power must 3 be raised to get 81?'
  • Step 2: Recognize that 81 can be written as a power of 3. Specifically, 81 = 3^4.
  • Step 3: Rewrite the logarithm using this power: log_3(81) = log_3(3^4).
  • Step 4: Use the property of logarithms that states log_b(b^x) = x. Here, b is 3 and x is 4.
  • Step 5: Apply this property: log_3(3^4) = 4.
  • Step 6: Conclude that the value of log_3(81) is 4.
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