2006 CJC Promo Q3 [Modified]

A graph with equation \(y=\mathrm{f}\left( x \right)\) undergoes \(3\) successive transformations as follows:

I: A scaling parallel to \(x\)-axis with scale factor \(\frac{1}{2}\),
II: A translation of \(3\) units in the direction of the positive \(x\)-axis,
III: A scaling parallel to \(y\)-axis with scale factor \(2\).

The resulting equation is \(y=2\ln \left( 2x-6 \right)\). Determine the equation of the graph \(y=\mathrm{f}\left( x \right)\), showing your workings clearly.