Log √3_(х-2)*log 5_х=2 log3_(х-2)

[latex]log _{ 3^{1/2} } (x-2)*log _{5}x=2log _{3}(x-2) [/latex] [latex]1/2*log _{ 3} (x-2)*log _{5}x=2log _{3}(x-2) [/latex] [latex]1/2*log _{ 3} (x-2)*log _{5}x-2log _{3}(x-2) =0[/latex] [latex]1/2*log _{ 3} (x-2)*(log _{5}x-4) =0[/latex] [latex]log _{ 3} (x-2)*(log _{5}x-4) =0[/latex] [latex]log _{ 3} (x-2)=0[/latex] х-2=1 х=3 [latex]log _{5}x-4 =0[/latex] [latex]log _{5}x =4[/latex] х=5⁴ х=625

решение во вложении----------------------------