Question

aflati x/y stiind ca 2lg(x-6y)=lgx+lgy

Answer 1

daca x>6*x si x,y >0 (existenta logaritmilor)
=> lg (x-6*y) ^2=lg x*y <=> (x-6*y)^2=x*y <=> x-6*y=rad(x*y) =>
=> x=rad(x*y) +6*y
=> x/y = (rad(x*y) +6*y) /y =rad(x*y) /y +6*y/y =rad(x)/rad (y) +6=
          = rad(x/y) +6

^ = la puterea
* = produs
/ =impartire
rad(x) =radical din x

Answer 2

$(x-6y)^{2}=xy \\ x-6y= \sqrt{xy} \\ \frac{x}{y} =6+ \frac{ \sqrt{x} }{ \sqrt{y} }$