Describe a sequence of two geometrical transformations that maps the graph of \(y = \ln x\) onto the graph of \(y = 4 \ln ( x - \mathrm { e } )\).
Sketch, on the axes given below, the graph of \(y = | 4 \ln ( x - \mathrm { e } ) |\), indicating the exact value of the \(x\)-coordinate where the curve meets the \(x\)-axis.
Solve the equation \(| 4 \ln ( x - e ) | = 4\).
Hence, or otherwise, solve the inequality \(| 4 \ln ( x - e ) | \geqslant 4\).
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