TeX Quellcode:
\begin{array}{ccl} \log_5\left(\genfrac{}{}{1pt}{}{\dfrac{375}{2a^6}}{\dfrac{3}{10x^2}}\right) &=& \log_5\left(\dfrac{375}{2a^6} : \dfrac{3}{10x^2}\right) \cr\cr &=& \log_5\left(\dfrac{375}{2a^6} \cdot \dfrac{10x^2}{3}\right) \cr\cr &=& \log_5\left(\dfrac{375 \cdot 10}{2 \cdot 3} \cdot \dfrac{x^2}{a^6}\right) \cr\cr &=& \log_5\left(625 \cdot \dfrac{x^2}{a^6}\right) \cr\cr &=& \log_5\left(625\right) + \log_5\left( \left(\dfrac{x}{a^3}\right)^2 \right) \cr\cr &=& 4+2\log_5\left(\dfrac{x}{a^3}\right) \cr &=& 4+2(\log_5(x)-\log_5\left(a^3\right)) \cr &=& 4+2(\log_5(x)-3\log_5(a)) \cr &=& 4+2\log_5(x)-6\log_5(a) \end{array}