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If log_a(3) = 0.5, what is the value of a? (2022)

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Question: If log_a(3) = 0.5, what is the value of a? (2022)

Options:

  1. 9
  2. 6
  3. 3
  4. 1.5

Correct Answer: 9

Exam Year: 2022

Solution: 

log_a(3) = 0.5 implies a^0.5 = 3, thus a = 3^2 = 9.

If log_a(3) = 0.5, what is the value of a? (2022)

Practice Questions

Q1
If log_a(3) = 0.5, what is the value of a? (2022)
  1. 9
  2. 6
  3. 3
  4. 1.5

Questions & Step-by-Step Solutions

If log_a(3) = 0.5, what is the value of a? (2022)
  • Step 1: Start with the equation log_a(3) = 0.5.
  • Step 2: Understand that log_a(3) means 'a raised to what power equals 3'.
  • Step 3: Rewrite the equation in exponential form: a^0.5 = 3.
  • Step 4: Recognize that 0.5 is the same as 1/2, so a^(1/2) = 3.
  • Step 5: To eliminate the exponent, square both sides of the equation: (a^(1/2))^2 = 3^2.
  • Step 6: Simplify the left side: a = 9.
  • Step 7: Conclude that the value of a is 9.
  • Logarithmic Equations – Understanding how to manipulate logarithmic equations to find the base.
  • Exponents – Applying properties of exponents to solve for the unknown variable.
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