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If log_a(5) = p and log_a(25) = q, what is the relationship between p and q?

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Question: If log_a(5) = p and log_a(25) = q, what is the relationship between p and q?

Options:

  1. q = 2p
  2. q = p/2
  3. q = p^2
  4. q = p + 1

Correct Answer: q = 2p

Solution: 

log_a(25) = log_a(5^2) = 2 log_a(5) = 2p, hence q = 2p.

If log_a(5) = p and log_a(25) = q, what is the relationship between p and q?

Practice Questions

Q1
If log_a(5) = p and log_a(25) = q, what is the relationship between p and q?
  1. q = 2p
  2. q = p/2
  3. q = p^2
  4. q = p + 1

Questions & Step-by-Step Solutions

If log_a(5) = p and log_a(25) = q, what is the relationship between p and q?
Correct Answer: q = 2p
  • Step 1: Understand the given information. We have two logarithmic equations: log_a(5) = p and log_a(25) = q.
  • Step 2: Recognize that 25 can be expressed as 5 squared (25 = 5^2).
  • Step 3: Use the property of logarithms that states log_a(b^c) = c * log_a(b).
  • Step 4: Apply this property to log_a(25): log_a(25) = log_a(5^2) = 2 * log_a(5).
  • Step 5: Substitute log_a(5) with p: log_a(25) = 2 * p.
  • Step 6: Since log_a(25) = q, we can write q = 2p.
  • Logarithmic Properties – Understanding the properties of logarithms, particularly the power rule which states that log_a(b^c) = c * log_a(b).
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