Question

лог2 1/3*лог3 1/5*лог5 1/2

Answer 1

$\log_2 \frac{1}{3}\log_3 \frac{1}{5}\log_5 \frac{1}{2} = (\log_2 1 - \log_2 3)(\log_3 1 - \log_3 5)(\log_5 1 - \log_5 2) = \\ = (-\log_2 3)(-\log_3 5)(-\log_5 2) = -\log_2 3\log_3 5\log_5 2 = \\ = - \frac{\log_{30} 3}{\log_{30} 2}*\frac{\log_{30} 5}{\log_{30} 3}*\frac{\log_{30} 2}{\log_{30} 5} = -1$