`a) D = (1; +infty)`
`log_{x - 1} (x^2 - 4x + 5) = 1`
`-> x^2 - 4x + 5 = x - 1`
`-> x^2 - 5x + 6 = 0`
`->` \(\left[ \begin{array}{l}x=3\\x=2\end{array} \right.\) `(TM)`
`-> S = {2; 3}`
`b) D = (0; 2) cup (3; +infty) \\ {1/2}`
`log_{2x} (x^2 - 5x + 6) = 2`
`-> x^2 - 5x + 6 = (2x)^2 = 4x^2`
`-> 3x^2 + 5x - 6 = 0`
`->` \(\left[ \begin{array}{l}x = \dfrac{\sqrt{97} - 5}{6}\\x= \dfrac{-\sqrt{97} - 5}{6} (l)\end{array} \right.\)
`-> S = {(\sqrt{97} - 5)/6}`
