TeX Quellcode:

\begin{array}{rclcl} 0 &=& \log_{314}(-k+9)+\log_{314}(4k) & \vert & \text{1. Logarithmengesetz} \\ 0 &=& \log_{314}\left((-k+9)\cdot 4k\right) \\0 &=& \log_{314}\left(-4k^2+36k\right) & \vert & 314^* \\ 1 &=& -4k^2+36k & \vert & -1 \\ 0 &=& -4k^2+36k-1 & \vert & :(-4) \\ 0 &=& k^2-9k+\frac{1}{4} & \vert & \text{p-q-Formel} \\ k_{1,2} &=& \dfrac{9}{2} \pm \sqrt{\dfrac{81}{4}-\dfrac{1}{4}} \\ &=& \dfrac{9}{2} \pm \sqrt{20} = \dfrac{9}{2}\pm\sqrt{4\cdot 5} \\\\ k_1 &=& \dfrac{9}{2} + 2\sqrt{5} \approx 8{,}97 \in \mathbb{D} \\ k_2 &=& \dfrac{9}{2} - 2\sqrt{5} \approx 0{,}03 \in \mathbb{D}\end{array}