Sketch \(y=2{{\mathrm{e}}^{2x+1}}-3\). Hence find the equation of the straight line which must be added on the graph of \(y=2{{\mathrm{e}}^{2x+1}}-3\) to solve the equation \(x+\ln \sqrt{2}=\frac{1}{2}\left[ \ln \left( 5-x \right)-1 \right]\).
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