[tex]( \frac{4}{9})^x*( \frac{27}{8})^{x-1} = \frac{2}{3},sau, ( \frac{4}{9})^x*( \frac{27}{8})^{x}* (\frac{27}{8})^{-1} = \frac{2}{3} [/tex], restrangem puterile si inmultim cu 27/8, obtinem: [tex]( \frac{4}{9}* \frac{27}{8})^x* \frac{8}{27}* \frac{27}{8}= \frac{2}{3}* \frac{27}{8} [/tex], facem simplificarile si obtinem: [tex]( \frac{3}{2})^x= \frac{9}{4} =( \frac{3}{2})^2 [/tex], deci x=2.
Am folosit egalitatea [tex] (\frac{27}{8})^{-1}= \frac{8}{27} [/tex]
