Question

Sa se rezolve ecuatia:
(4/9)^x * (27/8)^x-1=2/3

Answer 1

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