In general, we can translate a function c units to the right by changing its argument this way:
[tex]f(x)\to f(x-c)[/tex]So, if we translate log(x) one unit to the right, we will get:
[tex]\log (x-1)[/tex]Now, in general, when we translate a function f(x) c units downwards, we obtain a new function, this is:
[tex]f(x)\to f(x)-c[/tex]Then, in our case, we have already translated the function one unit to the right, after applying the translation downwards, we get:
[tex]g(x)=\log (x-1)-2[/tex]This is the function once we have transformed it
Finally, we need the graph that matches this equation, for this look at the value of x=2
[tex]\begin{gathered} x=2 \\ \Rightarrow g(2)=\log (1)-2=-2 \\ \Rightarrow(2,-2) \end{gathered}[/tex]The graph must contain the point (2,-2). Thus, only the graph on the right top corner can be the graph of the function. The graph on the right top corner is the answer