Given equations are : `2^a + 3^b = 17, 2^2 - 3. 3^b = 5` `or x + y = 17 & 4x - 3y = 5,` where `x = 2^a & y = 3^b.` On solving, we get : x = 8 and y = 9. `:. 2^a = 8 = 2^3` and` 3^b = 9 = 3^2` :. a = 3 and b = 2