Variables \(x\) and \(y\) are such that when \(\mathrm e^{4y}\) is plotted against \(x\), a straight line of gradient \(\frac25\), passing through \((10,2)\), is obtained.

(a) Find \(y\) in terms of \(x\).

(b) Find the value of \(y\) when \(x=45\), giving your answer in the form \(\ln p\).

(c) Find the values of \(x\) for which \(y\) can be defined.