If \(log_a 3\) = m and \(log_a 5\) = p, find \(log_a 75\)
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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