Ecuatia se poate scrie: [tex] \frac{2}{3}*( \frac{2}{3})^x+ \frac{2}{3}* \frac{1}{( \frac{2}{3})^x }= \frac{13}{9} [/tex]. Substituim pe [tex] (\frac{2}{3})^x=y [/tex], impartim ecuatia cu [tex] \frac{2}{3} [/tex], se obtine ec. [tex]y+ \frac{1}{y}= \frac{13}{6},adica,y^{2}- \frac{13}{6}y+1=0 [/tex], avem Δ=([tex]( \frac{13}{6})^2-4= \frac{25}{36}, [/tex], radacinile sunt: y=2/3 si y=3/2, deci [tex] x_{1}=1,si, x_{2}=-1 [/tex]
