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If log_4(16) = x, what is the value of x?

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Question: If log_4(16) = x, what is the value of x?

Options:

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Correct Answer: 2

Solution: 

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

If log_4(16) = x, what is the value of x?

Practice Questions

Q1
If log_4(16) = x, what is the value of x?
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Questions & Step-by-Step Solutions

If log_4(16) = x, what is the value of x?
  • Step 1: Understand that log_4(16) means 'to what power must 4 be raised to get 16?'
  • Step 2: Recognize that 16 can be written as 4 raised to a power. Specifically, 16 = 4^2.
  • Step 3: Rewrite the logarithm using this information: log_4(16) = log_4(4^2).
  • Step 4: Use the property of logarithms that states log_b(b^a) = a. Here, b is 4 and a is 2.
  • Step 5: Therefore, log_4(4^2) = 2.
  • Step 6: Conclude that x = 2.
  • Logarithms – Understanding the relationship between exponents and logarithms, specifically how to evaluate logarithms with different bases.
  • Change of Base – Recognizing that logarithms can be expressed in terms of powers, which simplifies the evaluation process.
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