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

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

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

Correct Answer: q = 2p

Step 1: Understand that log_a(5) = p means that 'a' raised to the power of 'p' equals 5.
Step 2: Recognize that log_a(25) can be rewritten because 25 is the same as 5 squared (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 we defined log_a(25) as q, we can say q = 2p.

Logarithmic Properties – Understanding the properties of logarithms, particularly the power rule which states that log_a(b^c) = c * log_a(b).