If \(log_a 3\) = m and \(log_a 5\) = p, find \(log_a 75\)
MATHEMATICS
WAEC 2023
If \(log_a 3\) = m and \(log_a 5\) = p, find \(log_a 75\)
- A. \(m^2 + p \)
- B. 2m + p
- C. m + 2p
- D. \(m + p^2\)
Correct Answer: C. m + 2p
Explanation
Given: \(log_a 3\) = m and \(log_a 5\) = p
\(log_a 75\) = \(log_a (3 × 25)\)
= \(log_a (3 × 5^2)\)
= \(log_a 3 + log_a 5^2\)
= \(log_a 3 + 2log_a 5\)
Since \(log_a 3\) = m and \(log_a 5\) = p
∴ \(log_a 75\) = m + 2p
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