Question 895150
<pre>
{{{2^(2x) - 3^(2y) = 55}}}

{{{(2^2)^x - (3^2)^y = 55}}}

{{{4^x - 9^y = 55}}}

So some power of 4 minus some power of 9 equals 55.

Some powers of 4 are 

{{{matrix(1,7,    4^1=4,",", 4^2=16,",", 4^3=64,",", 4^4=256)}}}

Some powers of 9 are 

{{{matrix(1,7,    9^1=9,",", 9^2=81,",", 9^3=729,",", 9^4=6561)}}}

It only takes a little while to look through those, ignoring the huge
ones, and to see that 64-9 = 55

{{{4^3 - 9^1 = 64-9 = 55}}}

So x=3, y=1

Edwin</pre>