Write each of the following in the form \(\log _ { a } k\), where \(k\) is an integer:
\(\log _ { a } 4 + \log _ { a } 10\);
\(\log _ { a } 16 - \log _ { a } 2\);
\(3 \log _ { a } 5\).
Use logarithms to solve the equation \(( 1.5 ) ^ { 3 x } = 7.5\), giving your value of \(x\) to three decimal places.
Given that \(\log _ { 2 } p = m\) and \(\log _ { 8 } q = n\), express \(p q\) in the form \(2 ^ { y }\), where \(y\) is an expression in \(m\) and \(n\).