TeX Quellcode:

\begin{array}{rclcl} 5\lg(x) &=& 3\lg(12)+\lg(32)-3(\lg(4)+\lg(3)) \cr\cr 5\lg(x) &=& 3\lg(12)+\lg(32)-3\lg(4)-3\lg(3) &\vert& \text{3. Logarithmengesetz} \cr\cr \lg(x^5) &=& \lg(12^3)+\lg(32)-\lg(4^3)-\lg(3^3) &\vert& \text{1. Logarithmengesetz} \cr\cr \lg(x^5) &=& \lg(12^3 \cdot 32)-\lg(4^3)-\lg(3^3) &\vert& \text{2. Logarithmengesetz} \cr\cr \lg(x^5) &=& \lg\left(\dfrac{12^3 \cdot 32}{4^3}\right)-\lg(3^3) &\vert& \text{2. Logarithmengesetz} \cr\cr \lg(x^5) &=& \lg\left(\dfrac{12^3 \cdot 32}{4^3 \cdot 3^3}\right) &\vert& \text{4. Potenzgesetz} \cr\cr \lg(x^5) &=& \lg\left(\dfrac{12^3 \cdot 32}{(4 \cdot 3)^3}\right) \cr\cr \lg(x^5) &=& \lg\left(\dfrac{12^3 \cdot 32}{12^3}\right) \cr\cr \lg(x^5) &=& \lg(32) &\vert& 10^{*} \cr\cr 10^{\lg(x^5)} &=& 10^{\lg(32)} \cr\cr x^5 &=& 32 &\vert& \sqrt[5]{} \cr\cr x &=& 2 \;\in\;\mathbb{D} \\\\ \mathbb{L} &=& \{2\} \end{array}