Shenghui nailed the issue on the head. In case you are not familiar with how to work this out, the first thing to do is to break up the equation so that you can get it entirely in terms of Log and Log. Here is your original equation in Mathematica format:

myEquality = Log[y/b] == Log[a x/b/1 + a x/b] + (-22/100 + (Log[a x/b])^2)

Now we want to apply these rules, which will break up the products and divisions:

{Log[a_/b_] -> Log[a] - Log[b], Log[a_* b_] -> Log[a] + Log[b]}

Apply the rules:

myNewEquality = myEquality//.{Log[a_/b_] -> Log[a] - Log[b], Log[a_* b_] -> Log[a] + Log[b]}

And now we can Solve for Log:

Solve[myNewEquality, Log[y]]

(*Output*)

{{Log[y] -> -(11/50) + Log[2] + Log[a] +

Log[x] + (Log[a] - Log[b] + Log[x])^2[/b]}}

This is the form you want to use for your model. To keep things simple, we will remove the logrithms while we solve the model, so Log will become newA and Log will become newX. You will need to run Log on your input data before runnning the model.

NonlinearModelFit[data, -(11/50) + Log[2] + newA +

newX + (newA - newB + newX)^2, {newA, newB}, newX]

Once you get the values for newA and newB, keep in mind that (newA = Log) which will allow you to solve for the original values.