There is a point (1,0) of the parent function f(x) = log x find the image point on f(x)= 5 log(x-2) which is the same as y= 5f(x) . I know how to do this by applying appropriate transformations, however how come when I use the the algebraic approach found here How to find corresponding coordinates? , it does not work?

The answer is I found is (0,3).

Thank you.