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If log_x(16) = 4, what is the value of x?

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Question: If log_x(16) = 4, what is the value of x?

Options:

  1. 2
  2. 4
  3. 8
  4. 16

Correct Answer: 4

Solution: 

log_x(16) = 4 implies x^4 = 16 => x^4 = 2^4 => x = 2.

If log_x(16) = 4, what is the value of x?

Practice Questions

Q1
If log_x(16) = 4, what is the value of x?
  1. 2
  2. 4
  3. 8
  4. 16

Questions & Step-by-Step Solutions

If log_x(16) = 4, what is the value of x?
Correct Answer: 2
  • Step 1: Start with the equation log_x(16) = 4.
  • Step 2: Understand that log_x(16) = 4 means that x raised to the power of 4 equals 16.
  • Step 3: Rewrite the equation as x^4 = 16.
  • Step 4: Recognize that 16 can be expressed as 2 raised to the power of 4, so rewrite the equation as x^4 = 2^4.
  • Step 5: Since the bases are the same (both are raised to the power of 4), we can set the bases equal to each other: x = 2.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to find the base.
  • Exponential Equations – Converting logarithmic forms to exponential forms to solve for unknowns.
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