TeX Quellcode:

\begin{array}{rclcl} \log_3(x-75)-3 &=& \log_3(x+3) &\vert& -\log_3(x+3)+3 \cr\cr \log_3(x-75)-\log_3(x+3) &=& 3 &\vert& \text{2. Logarithmengesetz} \cr\cr \log_3\left(\dfrac{x-75}{x+3}\right) &=& 3 &\vert& 3^{*} \cr\cr 3^{\log_3\left(\dfrac{x-75}{x+3}\right)} &=& 3^3 \cr\cr \dfrac{x-75}{x+3} &=& 27 &\vert& \cdot (x+3)\cr x-75 &=& 27(x+3) \cr x-75 &=& 27x+81 &\vert& +75-27x \cr -26x &=& 156 &\vert& :\left(-26\right) \cr x &=& -6 \; \not \in \; \mathbb{D} \cr\cr & \mathbb{L} = \emptyset \end{array}