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If log_a(b) = p and log_a(c) = q, what is log_a(bc)?

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Question: If log_a(b) = p and log_a(c) = q, what is log_a(bc)?

Options:

  1. p + q
  2. pq
  3. p - q
  4. p/q

Correct Answer: p + q

Solution: 

log_a(bc) = log_a(b) + log_a(c) = p + q.

If log_a(b) = p and log_a(c) = q, what is log_a(bc)?

Practice Questions

Q1
If log_a(b) = p and log_a(c) = q, what is log_a(bc)?
  1. p + q
  2. pq
  3. p - q
  4. p/q

Questions & Step-by-Step Solutions

If log_a(b) = p and log_a(c) = q, what is log_a(bc)?
Correct Answer: p + q
  • Step 1: Understand that log_a(b) = p means that a raised to the power of p equals b.
  • Step 2: Understand that log_a(c) = q means that a raised to the power of q equals c.
  • Step 3: Recognize that bc means b multiplied by c.
  • Step 4: Use the property of logarithms that states log_a(bc) = log_a(b) + log_a(c).
  • Step 5: Substitute the values from Step 1 and Step 2 into the equation: log_a(bc) = p + q.
  • Logarithmic Properties – Understanding the property that states log_a(bc) = log_a(b) + log_a(c), which is a fundamental rule of logarithms.
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