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17. $\log _{x} \sqrt{5}+\log _{x}(5 x)-2.25=\left(\log _{x} \sqrt{5}\right)^{2}$.

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Official solution

17. Simple transformations lead to the equation

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

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.