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If log_a(16) = 4, what is the value of a? (2021)

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Question: If log_a(16) = 4, what is the value of a? (2021)

Options:

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

Correct Answer: 2

Exam Year: 2021

Solution: 

log_a(16) = 4 implies a^4 = 16. Since 16 = 2^4, we have a^4 = 2^4, thus a = 2.

If log_a(16) = 4, what is the value of a? (2021)

Practice Questions

Q1
If log_a(16) = 4, what is the value of a? (2021)
  1. 2
  2. 4
  3. 8
  4. 16

Questions & Step-by-Step Solutions

If log_a(16) = 4, what is the value of a? (2021)
  • Step 1: Start with the equation log_a(16) = 4.
  • Step 2: Understand that log_a(16) = 4 means that a raised to the power of 4 equals 16.
  • Step 3: Rewrite the equation as a^4 = 16.
  • Step 4: Recognize that 16 can be expressed as 2 raised to the power of 4, so rewrite it: a^4 = 2^4.
  • Step 5: Since both sides of the equation have the same exponent (4), we can set the bases equal to each other: a = 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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