[tex]log_5^210-log_510\cdot log_54+log_5^22=1\\\\L=log_5^210-log_510\cdot log_54+log_5^22=\\\\log_5^210-log_510\cdot log_52^2+log_5^22=\\\\log_5^210-2log_510\cdot log_52+log_5^22=\\\\(log_510-log_52)^2=\\\\(log_5(10:2))^2=\\\\(log_55)^2=1^2=1=P[/tex]
