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 is C
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
