TeX Quellcode:

\begin{array}{rclcl}5\ln(-7+13x)+5\ln\left(\dfrac{x^2}{13x-7}\right)-10 &=& 0 &\vert& +10 \\\\5\ln(-7+13x)+5\ln\left(\dfrac{x^2}{13x-7}\right) &=& 10 &\vert& :5 \\\\\ln(-7+13x)+\ln\left(\dfrac{x^2}{13x-7}\right) &=& 2 &\vert& \text{1. Logarithmengesetz} \\\\\ln\left(\left(-7+13x\right)\cdot \dfrac{x^2}{13x-7} \right) &=& 2 \\\\\ln\left(x^2\right) &=& 2 &\vert& \text{3. Logarithmengesetz} \\\\2\ln\left(x\right) &=& 2 &\vert& :2 \\\ln\left(x\right) &=& 1 &\vert& e^* \\x &=& e \in\mathbb{D}\end{array}