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

Sketch the graph of \(y=\ln \sqrt{3x-1}\) for \(x>\frac{1}{3}\). Find the equation of the straight line which must be added on the graph of \(y=\ln \sqrt{3x-1}\) to solve the equation \({{\mathrm{e}}^{3x}}+{{\mathrm{e}}^{4}}=3x{{\mathrm{e}}^{4}}\).