<s>[INST] Solve the inequality for $x$: $\log_4 (x^2 − 2x + 1) < \log_2 3$ Solve the inequality for $x$: $$\log_4 (x^2 − 2x + 1) < \log_2 3$$
I got two answers and I'm not sure if I did it correctly. 
1st ans: $(-2,1)\cup (1,4)$ 
2nd ans: $x \neq -2,4$
 [/INST] \begin{array}{c}
   \log_4 (x^2 − 2x + 1) < \log_2 3 \\
   x^2 − 2x + 1 < 4^{\log_2 3} \\
   0<(x-1)^2 < 2^{2\log_2 3} \\
   0<(x-1)^2 < 2^{\log_2 3^2} \\
   0<(x-1)^2 < 3^2 \\
   \text{$-3 < x-1 < 3$ and $x \ne 1$}  \\
   \text{$-2 < x < 4$ and $x \ne 1$} \\
   x \in (-2,1) \cup (1,4)
\end{array}
</s>