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If log_4(256) = x, what is the value of x? (2022)

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Question: If log_4(256) = x, what is the value of x? (2022)

Options:

  1. 4
  2. 5
  3. 6
  4. 8

Correct Answer: 8

Exam Year: 2022

Solution: 

log_4(256) = log_4(4^4) = 4.

If log_4(256) = x, what is the value of x? (2022)

Practice Questions

Q1
If log_4(256) = x, what is the value of x? (2022)
  1. 4
  2. 5
  3. 6
  4. 8

Questions & Step-by-Step Solutions

If log_4(256) = x, what is the value of x? (2022)
  • Step 1: Understand that log_4(256) means 'to what power must 4 be raised to get 256?'
  • Step 2: Rewrite 256 as a power of 4. We know that 4^4 = 256.
  • Step 3: Now we can say log_4(256) = log_4(4^4).
  • Step 4: According to the properties of logarithms, log_b(b^n) = n. So, log_4(4^4) = 4.
  • Step 5: Therefore, x = 4.
  • Logarithms – Understanding how to convert between exponential and logarithmic forms, and how to simplify logarithmic expressions.
  • Base Change – Recognizing that logarithms can be expressed in terms of powers of their base.
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