Solve $(\log_5 x)^2 - 3\log_5(x) + 2 = 0$.
I tried to solve this question but got stuck:
\begin{align} (\log_5 x)^2 - 3\log_5(x) + 2 &= 0 \\ (\log_5 x)^2 &= \log_5(x^3) - 2 \\ \log_{(\log_5 x)}(\log_5 x)^2 &= \log_{( \log_5 x)}(\log_5(x^3) - \log_5 25) \\ 2 &= \log_{(\log_5 x)}\left( \log_5\frac{x^3}{25} \right) \end{align}
Was my approach wrong? Where do I go from here?