(a) (i) Find the set of values of \(x\) for which \(\lg(5x-3)\) exists.

(ii) Solve the equation \(\lg(5x-3)=1\).

(b) Given that \(y\gt 0\) and \(\log_y x=4+\frac12\log_y 64+\log_y 162\), find \(y\) in terms of \(x\), giving your answer in its simplest form.