Question

Va rog frumos sa ma ajutati
Dau coroana

Answer 1

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