Using the definition of \(\cosh x\) in terms of \(\mathrm { e } ^ { x }\) and \(\mathrm { e } ^ { - x }\), prove that
$$\cosh 2 x = 2 \cosh ^ { 2 } x - 1$$
Hence solve the equation
$$\cosh 2 x - 7 \cosh x = 3$$
giving your answer in logarithmic form.