By using the definition of \(\sinh x\) in terms of \(\mathrm { e } ^ { x }\) and \(\mathrm { e } ^ { - x }\), show that
$$\sinh ^ { 3 } x = \frac { 1 } { 4 } \sinh 3 x - \frac { 3 } { 4 } \sinh x$$
Find the range of values of the constant \(k\) for which the equation
$$\sinh 3 x = k \sinh x$$
has real solutions other than \(x = 0\).
Given that \(k = 4\), solve the equation in part (ii), giving the non-zero answers in logarithmic form.