impartim toti termenii ecuatiei la [tex] 16^{x} [/tex]
[tex]4*( \frac{9}{4} )^{2x}-12*( \frac{9}{4})^x +9=0 \\ notam: (\frac{9}{4})^x=t,t\ \textgreater \ 0 \\ 4t^2-12t+9=0 [/tex]
Δ=0
[tex] t_{1}= t_{2}= \frac{12}{8}= \frac{3}{2} [/tex]
revenim la substitutie
[tex] (\frac{9}{4})^x = \frac{3}{2} \\ ( \frac{3}{2}) ^{2x}= \frac{3}{2} \\ 2x=1 \\ x= \frac{1}{2} [/tex]
