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If log_a(4) = 2, what is the value of a?

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Question: If log_a(4) = 2, what is the value of a?

Options:

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

Correct Answer: 4

Solution: 

log_a(4) = 2 implies a^2 = 4 => a = 2.

If log_a(4) = 2, what is the value of a?

Practice Questions

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

Questions & Step-by-Step Solutions

If log_a(4) = 2, what is the value of a?
Correct Answer: 2
  • Step 1: Understand the equation log_a(4) = 2. This means that 'a' raised to the power of 2 equals 4.
  • Step 2: Rewrite the equation in exponential form: a^2 = 4.
  • Step 3: Solve for 'a' by taking the square root of both sides: a = √4.
  • Step 4: Calculate the square root of 4, which is 2.
  • Step 5: Conclude that the value of 'a' is 2.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to find the base.
  • Exponential Relationships – Recognizing the relationship between logarithms and exponents.
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