TeX Quellcode:
\begin{array}{rclcl} \ln\left(\sqrt{5x+2}\right)+\ln\left((5x+2)^2\right) &=& 1 \cr \ln\left((5x+2)^{\frac{1}{2}}\right)+\ln\left((5x+2)^2\right) &=& 1 &\vert& \text{3. Logarithmengesetz} \cr \dfrac{1}{2}\ln(5x+2)+2\ln(5x+2) &=& 1 \cr \dfrac{5}{2}\ln(5x+2) &=& 1 &\vert& :\dfrac{5}{2} \cr \ln(5x+2) &=& \dfrac{2}{5} &\vert& e^{*} \cr e^{\ln(5x+2)} &=& e^{\frac{2}{5}} \cr 5x+2 &=& e^{\frac{2}{5}} &\vert& -2 \cr 5x &=& e^{\frac{2}{5}}-2 &\vert& : 5 \cr x &=& \dfrac{e^{\frac{2}{5}}-2}{5} \approx -0{,}10 \;\in\;\mathbb{D} \\\\ \mathbb{L} &=& \left\{\dfrac{e^{\frac{2}{5}}-2}{5}\right\} \end{array}