Question

Sa se rezolve in multimea numerelor reale ecuatia 9^(x)-10*3^(x-1)+1=0

Answer 1

9=3²
3^(x-1)=3^x/3   ecuatia devine
3^2x-10/3*3^x+1=0
Substitutie
3^x=y>0
y^2-10y/3+1=0
aduci  la  acelasi   numitor
3y²-10y+3=0
y1=-1/3 => 3^x=-1/3 => x=-1
y2=7/3
3^x=7/3
x=log(3)(7/3)