TeX Quellcode:

\begin{array}{lrclcll}& 0 &=& 3x\log_8\left(2\right)+x\log_8\left(2x\right)+2x\log_8\left(10x\right) \\\\& 0 &=& x\left[3\log_8\left(2\right)+\log_8\left(2x\right)+2\log_8\left(10x\right)\right] &\vert& \text{3. Logarithmengesetz} \\\\& 0 &=& x\left[\log_8\left(2^3\right)+\log_8\left(2x\right)+\log_8\left((10x)^2\right)\right] \\\\& 0 &=& x\left[\log_8(8)+\log_8(2x)+\log_8\left(100x^2\right)\right] &\vert& \text{2. Logarithmengesetz}\\\\& 0 &=& x\cdot \log_8\left(8\cdot 2x\cdot 100x^2\right) \\& 0 &=& x\cdot \log_8\left(1.600x^3\right) & \vert & \text{Satz vom Nullprodukt}\\\\\text{Faktor 1:} & x_1 &=& 0 \not\in\mathbb{D} \\\\\text{Faktor 2:} & \log_8\left(1.600x^3\right) &=& 0 &\vert& 8^{*}\\& 1.600x^3 &=& 1 &\vert& :1.600 \\& x^3 &=& \dfrac{1}{1.600} &\vert &\sqrt[3]{} \\\\& x_2 &=& \sqrt[3]{\dfrac{1}{1.600}} \approx 0{,}09 \;\in\;\mathbb{D}\end{array}