17. $\log _{x} \sqrt{5}+\log _{x}(5 x)-2.25=\left(\log _{x} \sqrt{5}\right)^{2}$.
17. Simple transformations lead to the equation

$\log _{x}^{2} 5-6 \log _{x} 5+5=0$. From which $x_{1}=\sqrt[5]{5}, x_{2}=5$.