Mathematics - Functions Question with Solution | TestHub

$\begin{array}{rlrl}& \text{ Let }& {\log }_2|x|& =t\dots (i)\\ & \therefore & \sqrt{5-t}& =3-t\\ \Rightarrow & & 5-t& =(3-t{)}^2\\ \Rightarrow & & 5-t& =9+t^2-6t\end{array}$ $\begin{array}{rl}& \Rightarrow t^2-5t+4=0\\ & \Rightarrow (t-4)(t-1)=0\\ & \Rightarrow t=1\text{ or }4\text{[rejected]}\\ & [\because \sqrt{5-4}=3-4,1\ne -1]\\ & \Rightarrow {\log }_2|x|=1\\ & \Rightarrow |x|=2\\ & \Rightarrow x=\pm 2\end{array}$ $\therefore$ Total 2 real solutions.