It's a transcendental (as opposed to algebraic, e.g. polynomial) equation in y, and Mathematica simply does not know of a way to solve it for y.
Solve[(1 + t)^y == x*((1 + g)^(y + 1) - 1)/g, y]
During evaluation of In[55]:= Solve::nsmet: This system cannot be solved with the methods available to Solve. >>
Out[55]= Solve[(1 + t)^y == ((-1 + (1 + g)^(1 + y)) x)/g, y]
Wasn't for lack of trying...
What this means, among other things, is that you didn't do anything wrong, other than perhaps having expectations too high for what could be done here.
