[latex]log^2_5 \frac{x}{5}+5 = 3log_5 x [/latex]

[latex]log^2_5 \frac{x}{5}+5=3log_5 x;\\\\x>0;\\\\(log_5 x-log_5 5)^2+5=3log_5 x;\\\\ (log_5 x-1)^2+5-3log_5 x=0;\\\\ log^2_5 x-2log_5 x+1+5-3log_5 x=0;\\\\ log^2_5 x-5log_5 x+6=0;\\\\ (log_5 x-2)(log_5 x-3)=0;\\\\ log_5 x-2=0;log_5 x=2;x=5^2;x_1=25;\\\\ log_5 x-3=0;log_5 x=3;x=5^3;x_2=125[/latex] отвте: 25, 125