Sketch the graph of \(y={{\mathrm{e}}^{2x}}-2\). Determine the equation of the straight line which must be drawn on the graph of \(y={{\mathrm{e}}^{2x}}-2\) to obtain a graphical solution of the equation \(x=\ln \sqrt{7-3x}\).

Exponential and Logarithmic Functions - Sketching Exponential Functions and Solving Equations Graphically

IP 3

Sketch the graph of \(y={{\mathrm{e}}^{2x}}-2\).
Determine the equation of the straight line which must be drawn on the graph of \(y={{\mathrm{e}}^{2x}}-2\) to obtain a graphical solution of the equation \(x=\ln \sqrt{7-3x}\).

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Answer:(i) Intercepts \((0,-1)\), \(\left(\dfrac{\ln2}{2},0\right)\); asymptote \(y=-2\). (ii) \(y=5-3x\).

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