Use the definitions of \(\cosh \theta\) and \(\sinh \theta\) in terms of \(\mathrm { e } ^ { \theta }\) to show that
$$\cosh x \cosh y - \sinh x \sinh y = \cosh ( x - y )$$
It is given that \(x\) satisfies the equation
$$\cosh ( x - \ln 2 ) = \sinh x$$
Show that \(\tanh x = \frac { 5 } { 7 }\).
Express \(x\) in the form \(\frac { 1 } { 2 } \ln a\).