Question

Find all a, b such that `a^2 9^b = 4` and `a/3^b =18`?

Answer 1

`(a,b) in {(6, -1)} subset ZZ^2`

Explanation:

`a = 18*3^b and (18*3^b)^2 * 3^(2b) = 4`

`324 * 3^(4b) = 4 => 81^b = 1/81 => b = -1`

`a = 18/3 = 6`