TeX Quellcode:

\begin{array}{lrclcl} & 0 &=& \dfrac{5}{4}\log_{10}\left(16e^x+1\right)\cdot \ln\left(x^3+9\right) &\vert& :\dfrac{5}{4} \\& 0 &=& \log_{10}\left(16e^x+1\right)\cdot \ln\left(x^3+9\right) &\vert& \text{Satz vom Nullprodukt} \\\\ \text{Faktor 1:} & 0 &=& \log_{10}\left(16e^x+1\right) &\vert& 10^* \\ & 1 &=& 16e^x+1 &\vert& -1 \\ & 0 &=& 16e^x &\vert& :16 \\& 0 &=& e^x &\vert& \ln() \\& \ln(0) &=& x_1 \\\\\text{Faktor 2:} & 0 &=& \ln(x^3+9) &\vert& e^* \\& 1 &=& x^3+9 &\vert& -9 \\ & -8 &=& x^3 &\vert& \sqrt[3]{} \\ & x_2 &=& -2 \in \mathbb{D} \end{array}