TeX Quellcode:

\begin{array}{rclcl} \log_2\left(16^x\right)+\log_5\left(25^{x^2}\right) &=& 16 &\vert& \text{3. Logarithmengesetz} \cr x\cdot \log_2(16)+x^2\cdot \log_5(25) &=& 16 &\vert& \text{Logarithmen berechnen} \cr 4x+2x^2 &=& 16 &\vert& -16 \cr 2x^2+4x-16 &=& 0 &\vert& :2 \cr x^2+2x-8 &=& 0 &\vert& \text{p-q-Formel} \cr x_{1,2} &=& -1 \pm \sqrt{1+8} \cr &=& -1 \pm \sqrt{9} \cr \cr x_1 &=& -1+3 = 2 \;\in\;\mathbb{D} \cr x_2 &=& -1-3 = -4 \;\in\;\mathbb{D} \\\\ \mathbb{L} &=& \{-4;2\} \end{array}