We can find an answer x=2, by trial and error,



But is that the only solution, and if so, why?









The function 
is strictly decreasing.  It has value 17 when x=0, 17 > 1, 
and value 43/125=0.344 when x=3, 0.344 < 1

Thus it can intersect the horizontal line y=1 only once.

So it has only one solution, x=2.

Edwin