- The point \(P\) lies on the curve with equation
$$y = 4 \mathrm { e } ^ { 2 x + 1 }$$
The \(y\)-coordinate of \(P\) is 8 .
- Find, in terms of \(\ln 2\), the \(x\)-coordinate of \(P\).
- Find the equation of the tangent to the curve at the point \(P\) in the form \(y = a x + b\), where \(a\) and \(b\) are exact constants to be found.