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Which of the following is the correct simplification of log_a(b^2)?

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Question: Which of the following is the correct simplification of log_a(b^2)?

Options:

  1. 2 log_a(b)
  2. log_a(2b)
  3. log_a(b) + 2
  4. log_a(b) - 2

Correct Answer: 2 log_a(b)

Solution: 

Using the power rule of logarithms, log_a(b^2) simplifies to 2 log_a(b).

Which of the following is the correct simplification of log_a(b^2)?

Practice Questions

Q1
Which of the following is the correct simplification of log_a(b^2)?
  1. 2 log_a(b)
  2. log_a(2b)
  3. log_a(b) + 2
  4. log_a(b) - 2

Questions & Step-by-Step Solutions

Which of the following is the correct simplification of log_a(b^2)?
  • Step 1: Identify the expression you want to simplify, which is log_a(b^2).
  • Step 2: Recall the power rule of logarithms, which states that log_a(x^n) = n * log_a(x).
  • Step 3: In your expression, b^2 is the same as x^n where x = b and n = 2.
  • Step 4: Apply the power rule: log_a(b^2) becomes 2 * log_a(b).
  • Step 5: Write the final simplified expression: 2 log_a(b).
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