TeX Quellcode:

\begin{array}{rclcl}0 &=& 2\log_{10}(5x)+3\log_{10}(x)+8 &\vert& \text{3. Logarithmengesetz} \\\\0 &=& \log_{10}(25x^2)+\log_{10}(x^3)+8 &\vert& 10^* \\\\ 1 &=& 10^{\log_{10}(25x^2)+\log_{10}(x^3)+8} \\\\ 1 &=& 10^{\log_{10}\left(25x^2\right)} \cdot 10^{\log_{10}(x^3)}\cdot 10^8 \\ 1 &=& 25x^2 \cdot x^3 \cdot 10^8 \\ 1 &=& 25 \cdot 10^8x^5 &\vert& :(25\cdot 10^8) \\ \dfrac{1}{25\cdot 10^8} &=& x^5 &\vert& \sqrt[5]{} \\ x &=& \sqrt[5]{\dfrac{1}{25\cdot 10^8}} \approx 0{,}01 \in \mathbb{D} \end{array}