SOLUTION: Dear Sir/Madam, Please help me with this question, Solve {{{2^(2x) - 3^(2y) = 55}}} for x and y are integers. Thank you very much!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Dear Sir/Madam, Please help me with this question, Solve {{{2^(2x) - 3^(2y) = 55}}} for x and y are integers. Thank you very much!      Log On


   

Question 895150: Dear Sir/Madam,
Please help me with this question,
Solve 2%5E%282x%29+-+3%5E%282y%29+=+55 for x and y are integers.

Thank you very much!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E%282x%29+-+3%5E%282y%29+=+55

%282%5E2%29%5Ex+-+%283%5E2%29%5Ey+=+55

4%5Ex+-+9%5Ey+=+55

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

Some powers of 4 are 



Some powers of 9 are 



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

4%5E3+-+9%5E1+=+64-9+=+55

So x=3, y=1

Edwin