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If log_4(x) = 3, find x.

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Question: If log_4(x) = 3, find x.

Options:

  1. 16
  2. 64
  3. 256
  4. 1024

Correct Answer: 64

Solution: 

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

If log_4(x) = 3, find x.

Practice Questions

Q1
If log_4(x) = 3, find x.
  1. 16
  2. 64
  3. 256
  4. 1024

Questions & Step-by-Step Solutions

If log_4(x) = 3, find x.
Correct Answer: 64
  • Step 1: Understand that log_4(x) = 3 means that 4 raised to the power of 3 equals x.
  • Step 2: Write the equation in exponential form: x = 4^3.
  • Step 3: Calculate 4^3, which means 4 multiplied by itself 3 times: 4 * 4 * 4.
  • Step 4: First, calculate 4 * 4 = 16.
  • Step 5: Now multiply 16 by 4: 16 * 4 = 64.
  • Step 6: Therefore, x = 64.
  • Logarithms – Understanding the relationship between logarithms and exponents, specifically how to convert from logarithmic form to exponential form.
  • Base of Logarithm – Recognizing the base of the logarithm (in this case, 4) and how it affects the calculation.
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