[tex] 2^{2x+1}+ 3^{2x+1}=5*2^x*3^x [/tex] ⇒[tex]2* 4^{x}+3*9^x=5*2^x*3^x [/tex], impartim ecuatia cu [tex] 9^{x} [/tex], si se obtine ecuatia :[tex]2*( \frac{4}{9})^x+3=5( \frac{6}{9})^x,deci:2*(( \frac{2}{3})^x)^2-5( \frac{2}{3})^x+3=0 [/tex], notam y=[tex] (\frac{2}{3})^x [/tex], cu conditia y>0, si obtine ec.:[tex]2y^2-5y+3=0. [/tex], cu radacinile: [tex] y_{1}=1,deci,1= (\frac{2}{3})^x,avem, x_{1}=0;si, y_{2}= \frac{3}{2}= (\frac{2}{3} )^{-1},deci. x_{2}=-1 [/tex]
