In[920]:= Clear[x, y, a]
Reduce[y == a^(x - 1) + a^(x - 2) + a^(x - 3), a]
During evaluation of In[920]:= Reduce::nsmet: This system cannot be solved with the methods available to Reduce. >>
Out[921]= Reduce[y == a^(-3 + x) + a^(-2 + x) + a^(-1 + x), a]