2. Solve the inequality $\log _{x}\left(25-40 x+16 x^{2}\right)<0$.
Solution: $\log _{x}\left(25-40 x+16 x^{2}\right)0, \quad x \neq 1, \quad x \neq 5 / 4$.

1) $01 \Leftrightarrow 2 x^{2}-5 x+3>0 ;\left\{\begin{array}{l}x3 / 2 \\ 01, \quad x \neq 5 / 4 ; 25-40 x+16 x^{2}<1 \Leftrightarrow 2 x^{2}-5 x+3<0 \Leftrightarrow 1<x<3 / 2, x \neq 5 / 4$.

Answer: $x \in(0 ; 1) \cup(1 ; 5 / 4) \cup(5 / 4 ; 3 / 2)$.