Question

Выражение с логарифмом

Answer 1

 $frac{log_{5}30}{log_{150}5} - frac{log_{5}750}{log_{6}5} = \\ frac{log_{5}30*log_{6}5-log_{5}750*log_{150}5}{log_{150}5*log_{6}5} = \\ frac{(log_{5}6+1)frac{1}{log_{5}6}-(log_{5}150+1)frac{1}{log_{5}150}}{frac{1}{log_{5}150*log_{5}6}}=\\ (log_{6}5-log_{150}5)(log_{5}150*log_{5}6)=(frac{1}{log_{5}6} - frac{1}{log_{5}150})(log_{5}150*log_{5}6)=\\ frac{log_{5}150-log_{5}6}{log_{5}6*log_{5}150}*log_{5}150*log_{5}6=\\ log_{5}frac{150}{6}=log_{5}25=2$