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

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

IP 3

Sketch \(y=\ln \left( 2-x \right)\). Find the equation of the straight line which must be drawn to solve the equation \(3{{\mathrm{e}}^{x}}-{{\left( 2-x \right)}^{3}}=0\).

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Answer:Sketch \(y=\ln(2-x)\) for \(x<2\), with asymptote \(x=2\) and intercepts \((1,0),(0,\ln2)\). Add \(y=\frac x3+\frac{\ln3}{3}\).

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