problem: Evaluate $\log_{\sqrt{5}} 125\sqrt{5}$.
solution: Let $x= \log_{\sqrt{5}}125\sqrt{5}$.  Putting this in exponential notation gives $(\sqrt{5})^x = 125\sqrt{5}$.  Writing both sides with 5 as the base gives us $5^{\frac{x}{2}} = 5^3\cdot 5^{\frac{1}{2}} = 5^{\frac{7}{2}}$, so $x/2=7/2$.  Therefore, $x=\boxed{7}$.