TeX Quellcode:

\begin{array}{rclclll}2\ln(x-1)+2\ln(3) &=& 2\ln(1)+3\ln(2) &\vert& \text{3. Logarithmengesetz} \\\ln\left((x-1)^2\right)+\ln\left(3^2\right) &=& 0+\ln\left(2^3\right) &\vert& -\ln\left(3^2\right) \\\ln\left((x-1)^2\right) &=& \ln\left(2^3\right)-\ln\left(3^2\right) &\vert& \text{2. Logarithmengesetz}\\\ln\left((x-1)^2\right) &=& \ln\left(\dfrac{2^3}{3^2}\right) &\vert& e^{*} \\(x-1)^2 &=& \dfrac{8}{9} &\vert& \pm\sqrt{} \\x-1 &=& \pm\sqrt{\dfrac{8}{9}} &\vert&+1 \\\\x_1 &=& 1+\dfrac{2\sqrt{2}}{3} \approx 1{,}94 \;\in\;\mathbb{D} \\ x_2 &=& 1-\dfrac{2\sqrt{2}}{3} \approx 0{,}06 \;\not\in\;\mathbb{D} \\ \\\mathbb{L} &=& \left\{1+\dfrac{2\sqrt{2}}{3}\right\}\end{array}