how to figure this out?

Here's a graphical solution

Note that we cannot take the log of 0  or a negative value

So  x^2 - 4x + 3    must be > 0

Thus....if we graph x^2 -4x +3 here  : https://www.desmos.com/calculator/8jbvusmqcq

We can note that the gragh is > 0   on these intervals

(-inf, 1)   and  (3, infinity)

Note that  answer "K"  seems to fit the bill....!!!!