[tex]\it \dfrac{3}{25^x-2}=5^{2x-1} \Rightarrow \dfrac{3}{(5^2)^x-2}=5^{2x}\cdot\dfrac{1}{5} \Rightarrow \dfrac{3}{5^{2x}-2}=\dfrac{5^{2x}}{5} \\ \\ \\ Not\breve am\ 5^{2x}=t,\ \ t>0,\ iar\ ecua\c{\it t}ia\ devine:\\ \\ \\ \dfrac{3}{t-2}=\dfrac{t}{5} \Rightarrow t^2-2t-15=0 \Rightarrow t^2-2t+1-16=0\Rightarrow (t-1)^2-4^2=0\Rightarrow \\ \\ \\ \Rightarrow (t-1-4)(t-1+4)=0 \Rightarrow (t-5)(t+3)=0\Rightarrow \begin{cases}\it t_1=-3,\ nu\ convine\\ \\ \it t_2=5\end{cases}[/tex]
[tex]\it Revenim\ asupra\ nota\c{\it t}iei:\\ \\ t=5 \Rightarrow 5^{2x}=5^1 \Rightarrow 2x=1 \Rightarrow x=\dfrac{1}{2}[/tex]
