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What is the value of log_4(16)?

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Question: What is the value of log_4(16)?

Options:

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  4. 4

Correct Answer: 2

Solution: 

log_4(16) = log_4(4^2) = 2.

What is the value of log_4(16)?

Practice Questions

Q1
What is the value of log_4(16)?
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Questions & Step-by-Step Solutions

What is the value of log_4(16)?
  • Step 1: Understand what log_4(16) means. It asks, 'To what power do we raise 4 to get 16?'
  • Step 2: Rewrite 16 as a power of 4. We know that 4^2 = 16.
  • Step 3: Now we can replace 16 in the log expression: log_4(16) becomes log_4(4^2).
  • Step 4: Use the property of logarithms that says log_b(b^x) = x. Here, b is 4 and x is 2.
  • Step 5: Therefore, log_4(4^2) = 2.
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