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If log_4(64) = x, what is the value of x?

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Question: If log_4(64) = x, what is the value of x?

Options:

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  2. 3
  3. 4
  4. 5

Correct Answer: 3

Solution: 

log_4(64) = log_4(4^3) = 3.

If log_4(64) = x, what is the value of x?

Practice Questions

Q1
If log_4(64) = x, what is the value of x?
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  2. 3
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Questions & Step-by-Step Solutions

If log_4(64) = x, what is the value of x?
Correct Answer: 3
  • Step 1: Understand that log_4(64) means 'to what power must 4 be raised to get 64?'
  • Step 2: Rewrite 64 as a power of 4. We know that 4^3 = 64.
  • Step 3: Now we can say log_4(64) = log_4(4^3).
  • Step 4: Use the property of logarithms that says log_b(b^a) = a. Here, b is 4 and a is 3.
  • Step 5: Therefore, log_4(4^3) = 3.
  • Step 6: Conclude that x = 3.
  • Logarithmic Functions – Understanding how to evaluate logarithms, particularly changing the base and using properties of exponents.
  • Exponential Relationships – Recognizing that logarithms can be expressed in terms of exponents, such as log_b(a^c) = c * log_b(a).
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