Exponential and Logarithmic Functions - Sketching Logarithmic Functions and Solving Equations Graphically
Exponential and Logarithmic Functions - Sketching Logarithmic Functions and Solving Equations Graphically
IP 3
The curve of \(y=a\ln \left( 2x-\operatorname{e} \right)+1\) passes through \(\left(\operatorname{e},4 \right)\). Find the value of \(a\).
Hence, sketch the graphs of \(y=a\ln \left( 2x+\operatorname{e} \right)+1\), labelling the coordinates of axial intercepts and equations of asymptotes.
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Answer:\(a=3\). For the requested plus-sign curve: asymptote \(x=-e/2\); intercepts \((0,4)\) and \(\left((e^{-1/3}-e)/2,0\right)\).
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