The diagram below shows the graphs of \(y={{\mathrm{e}}^{2x}}\) and \(y=2{{\mathrm{e}}^{x}}\). Identify each graph and explain your answer. By drawing a suitable line on the diagram, state the number of solutions to each equation . \(2{{\mathrm{e}}^{x}}=-1\) \(2x-\ln 5=\ln \left( 2x+1 \right)\)

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

IP 3

The diagram below shows the graphs of \(y={{\mathrm{e}}^{2x}}\) and \(y=2{{\mathrm{e}}^{x}}\).

Identify each graph and explain your answer.
By drawing a suitable line on the diagram, state the number of solutions to each equation .
1. \(2{{\mathrm{e}}^{x}}=-1\)
2. \(2x-\ln 5=\ln \left( 2x+1 \right)\)

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Answer:(a) no real solution; (b) two real solutions

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