Решите log5 160*log5 6,4=

[latex]log_5160\cdot log_56,4=log_5(5\cdot 32)\cdot log_5\frac{64}{10}=(log_55+log_52^5)\cdot log_5\frac{32}{5}=\\\\=(1+5\cdot log_52)\cdot (log_52^5-log_55)=(1+5log_52)(5log_52-1)=\\\\=(5log_52)^2-1^2=25log^2_52-1[/latex] [latex]log_5160-log_56,4=1+5log_52-(5log_52-1)=2[/latex]