13. \((1 - \log_8 10)(1 - \log_8 40)\)

\((1 - \log_8 10)(1 - \log_8 40) = (1 - \log_8 10)(1 - (\log_8 5 + \log_8 8) )= (1 - \log_8 10)(1 - \log_8 5 - 1) = (1 - \log_8 10)( - \log_8 5)= \log_8 10\cdot \log_8 5 - \log_8 5 = \log_8 5(\log_8 10 -1) = \log_8 5(\log_8 10 - \log_8 8)=\log_8 5 \cdot \log_8 (\frac{10}{8})=\log_8 5 \cdot \log_8 (\frac{5}{4}) = \log_8 5 \cdot (\log_8 5 - \log_8 4) = (\log_8 5)^2 - \log_8 5 \cdot log_8 4\)