3.21: Linear law: $e^{4y}$ against $x$

Variables $x$ and $y$ are such that when $e^{4y}$ is plotted against $x$, a straight line of gradient $\tfrac{5}{2}$, passing through $(10, 2)$, is obtained.

Find $y$ in terms of $x$.

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

Find the values of $x$ for which $y$ can be defined.