3. Solve the equation $\log _{x}(5 \cdot \sqrt{5})-\frac{5}{4}=\left(\log _{x} \sqrt{5}\right)^{2}$.
3. We can simplify the equation to $\frac{3}{2} \log _{x} 5-\frac{5}{4}=\left(\frac{1}{2} \log _{x} 5\right)^{2}$. If we let $\log _{x} 5=t$ and simplify the equation, we get $t^{2}-6 t+5=0$, which has solutions $t_{1}=1$ and $t_{2}=5$. From $\log _{x} 5=1$ we get $x_{1}=5$, and from $\log _{x} 5=5$ we get $x^{5}=5$ or $x_{2}=\sqrt[5]{5}$.

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