Sketch the graph of \(y = \frac { 1 } { 2 ^ { x } }\), indicating the value of the intercept on the \(y\)-axis.
Use logarithms to solve the equation \(\frac { 1 } { 2 ^ { x } } = \frac { 5 } { 4 }\), giving your answer to three significant figures.
Given that
$$\log _ { a } \left( b ^ { 2 } \right) + 3 \log _ { a } y = 3 + 2 \log _ { a } \left( \frac { y } { a } \right)$$
express \(y\) in terms of \(a\) and \(b\).
Give your answer in a form not involving logarithms.