5 The curves \(C _ { 1 } : y = \cosh x\) and \(C _ { 2 } : y = \sinh 2 x\) intersect at the point where \(x = a\).
- Find the exact value of \(a\), giving your answer in logarithmic form.
- Sketch \(C _ { 1 }\) and \(C _ { 2 }\) on the same diagram.
- Find the exact value of the length of the arc of \(C _ { 1 }\) from \(x = 0\) to \(\mathrm { x } = \mathrm { a }\).