TeX Quellcode:

\begin{array}{rclcl}0 &=& \dfrac{\log_4(-x+47)}{\log_4(e) \cdot \ln(-x+47)}\cdot \left(-14x^2+56x+98\right) &\vert & \text{Basistransformation} \\\\0 &=& \dfrac{\log_4(-x+47)}{\log_4(e) \cdot \frac{\log_4(-x+47)}{\log_4(e)}}\cdot \left(-14x^2+56x+98\right) \\\\0 &=& \dfrac{\log_4(-x+47)}{1 \cdot \log_4(-x+47)}\cdot \left(-14x^2+56x+98\right) \\\\0 &=& 1 \cdot \left(-14x^2+56x+98\right) \\\\0 &=& -14x^2+56x+98 &\vert & :(-14) \\0 &=& x^2-4x-7 &\vert & \text{p-q-Formel} \\x_{1,2} &=& 2 \pm \sqrt{4+7} \\ x_{1,2} &=& 2 \pm \sqrt{11} \\\\x_{1} &=& 2 + \sqrt{11} \approx 5{,}32 \in \mathbb{D} \\x_{2} &=& 2 - \sqrt{11} \approx -1{,}32 \in \mathbb{D}\end{array}