Sketch the graph of $y=\ln x$. In order to solve the equation \({{x}^{2}}={{\operatorname{e}}^{2x-

Question

Sketch the graph of $y=\ln x$. In order to solve the equation ${{x}^{2}}={{\operatorname{e}}^{2x-3}}$, a suitable straight line has to be drawn on the same diagram as the graph of $y=\ln x$. Find the equation of the straight line and the number of solutions to the equation.

Accepted Answer

Three distinct real solutions: two positive and one negative. The graph of $\ln x$ alone shows only the positive solutions.

Solving Equation Graphically

Solving Equation Graphically

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