[tex]\log^2_{2}(x-1)^2-\log_{0,5} (x-1)\ \textgreater \ 5\\
4\log^2_{2}(x-1)-\log_{\frac{1}{2}}(x-1)\ \textgreater \ 5\\
4\log^2_2(x-1)+\log_2 (x-1)-5\ \textgreater \ 0\\
\log_{2}(x-1)\stackrel{not}{=}t\\
4t^2+t-5\ \textgreater \ 0\\
\Delta=1+4\cdot 4\cdot 5=81\Rightarrow \sqrt{\Delta}=9\\
t_1=\dfrac{-1+9}{8}=1\\
t_2=\dfrac{-1-9}{8}=-\dfrac{5}{4}\\
\text{Faci tabel de semn si iti dai seama ca }t\in \left(-\infty,-\dfrac{5}{4}\right)\cup \left(1,\infty\right)\\
\text{Deci }x\in \left(1,1+2^{-\frac{5}{4}}\right)\cup (3,\infty)\\
\text{Raspunsul este b)} [/tex]
