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

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

Options:

  1. c * log_a(b)
  2. log_a(c) * log_a(b)
  3. log_a(b) / c
  4. log_a(c^b)

Correct Answer: c * log_a(b)

Solution: 

The property of logarithms states that log_a(b^c) = c * log_a(b).

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

Practice Questions

Q1
Which of the following is the correct simplification of log_a(b^c)?
  1. c * log_a(b)
  2. log_a(c) * log_a(b)
  3. log_a(b) / c
  4. log_a(c^b)

Questions & Step-by-Step Solutions

Which of the following is the correct simplification of log_a(b^c)?
  • Step 1: Identify the expression you want to simplify, which is log_a(b^c).
  • Step 2: Recall the property of logarithms that states log_a(x^y) = y * log_a(x).
  • Step 3: In your expression, b is x and c is y.
  • Step 4: Apply the property: Replace x with b and y with c in the property.
  • Step 5: Write the simplified expression: log_a(b^c) = c * log_a(b).
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