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Which of the following logarithmic expressions is equivalent to log_2(8) - log_2

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Question: Which of the following logarithmic expressions is equivalent to log_2(8) - log_2(4)?

Options:

  1. log_2(2)
  2. log_2(1)
  3. log_2(0)
  4. log_2(3)

Correct Answer: log_2(2)

Solution: 

Using the property of logarithms that states log_a(b) - log_a(c) = log_a(b/c), we find log_2(8) - log_2(4) = log_2(8/4) = log_2(2).

Which of the following logarithmic expressions is equivalent to log_2(8) - log_2

Practice Questions

Q1
Which of the following logarithmic expressions is equivalent to log_2(8) - log_2(4)?
  1. log_2(2)
  2. log_2(1)
  3. log_2(0)
  4. log_2(3)

Questions & Step-by-Step Solutions

Which of the following logarithmic expressions is equivalent to log_2(8) - log_2(4)?
  • Step 1: Identify the logarithmic expressions we have: log_2(8) and log_2(4).
  • Step 2: Recall the property of logarithms that states log_a(b) - log_a(c) = log_a(b/c).
  • Step 3: Apply this property to our expressions: log_2(8) - log_2(4) becomes log_2(8/4).
  • Step 4: Calculate the division inside the logarithm: 8 divided by 4 equals 2.
  • Step 5: Now we have log_2(2).
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