TeX Quellcode:
\begin{array}{rclcl}0 &=& \ln\left(\dfrac{3z}{44z+11}\right)-\ln\left(-\dfrac{9}{22z}\right) &\vert& \text{2. Logarithmengesetz} \\ 0 &=& \ln\left(\dfrac{3z}{44z+11} : \left(-\dfrac{9}{22z}\right)\right) \\0 &=& \ln\left(\dfrac{3z}{11(4z+1)}\cdot \left(-\dfrac{22z}{9}\right)\right) \\0 &=& \ln\left(-\dfrac{2z^2}{12z+3}\right) &\vert& e^*\\ 1 &=& -\dfrac{2z^2}{12z+3} &\vert& \cdot (12z+3) \\ 12z+3 &=& -2z^2 &\vert& -12z-3 \\ 0 &=& -2z^2-12z-3 &\vert& :(-2) \\ 0 &=& z^2+6z+\dfrac{3}{2} &\vert& \text{p-q-Formel} \\\\z_{1,2} &=& -3 \pm \sqrt{3^2-\dfrac{3}{2}} \\ z_{1,2} &=& -3 \pm \sqrt{\dfrac{15}{2}} \\\\ z_{1} &=& -3+\sqrt{\dfrac{15}{2}} \approx -0{,}26 \in \mathbb{D} \\\\ z_{2} &=& -3-\sqrt{\dfrac{15}{2}} \approx -5{,}74 \in \mathbb{D} \\\end{array}