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Which of the following logarithmic properties is used to simplify log_a(b^c)?

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Question: Which of the following logarithmic properties is used to simplify log_a(b^c)?

Options:

  1. Power Rule
  2. Product Rule
  3. Quotient Rule
  4. Change of Base Formula

Correct Answer: Power Rule

Solution: 

The Power Rule states that log_a(b^c) = c * log_a(b).

Which of the following logarithmic properties is used to simplify log_a(b^c)?

Practice Questions

Q1
Which of the following logarithmic properties is used to simplify log_a(b^c)?
  1. Power Rule
  2. Product Rule
  3. Quotient Rule
  4. Change of Base Formula

Questions & Step-by-Step Solutions

Which of the following logarithmic properties is used to simplify log_a(b^c)?
  • Step 1: Identify the expression you want to simplify, which is log_a(b^c).
  • Step 2: Recall the Power Rule of logarithms, which states that log_a(b^c) can be rewritten.
  • Step 3: According to the Power Rule, you can move the exponent 'c' in front of the logarithm.
  • Step 4: Rewrite the expression using the Power Rule: log_a(b^c) becomes c * log_a(b).
  • Step 5: Confirm that you have simplified the expression correctly using the Power Rule.
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