f(x)=ln(1/(x-4)) is not an equation; it's a definition of a function.
A function has an argument, often represented by the letter x which appears in the definition (on the right side of equals) and tells us what process has to be carried out on the argument. So, for example, a question might follow that says "evaluate f(5)". This requires x to be replaced by the number 5. In this case, f(5)=ln(1/(5-4)). so f(5)=ln(1/1)=ln(1)=0. So f(5)=0.