TeX Quellcode:

\begin{array}{rclcl}\dfrac{\log_4(x-3)}{\log_4(x)} &=& -1 &\vert& \cdot \log_4(x) \\\log_4(x-3) &=& -\log_4(x) \\\log_4(x-3) &=& \log_4\left(x^{-1}\right) &\vert& 4^* \\x-3 &=& x^{-1} &\vert& \cdot x \\x^2-3x &=& 1 &\vert& -1 \\x^2-3x-1 &=& 0 &\vert& \text{p-q-Formel} \\x_{1,2} &=& \dfrac{3}{2} \pm \sqrt{\left(-\dfrac{3}{2}\right)^2+1} \\x_{1,2} &=& \dfrac{3}{2} \pm \sqrt{\dfrac{13}{4}} \\\\x_1 &=& \dfrac{3}{2}+\sqrt{\dfrac{13}{4}} \approx 3{,}30 \in \mathbb{D} \\x_2 &=& \dfrac{3}{2}-\sqrt{\dfrac{13}{4}} \approx -0{,}30 \not \in \mathbb{D} \\\\\mathbb{L} &=& \left\{\dfrac{3}{2}+\sqrt{\dfrac{13}{4}}\right\}\end{array}