\(314_{10} - 256_7 = 340_x\) Convert 2567 and 340x to base 10, such that: 314 - 139 = 3x\(^2\) + 4x => \(3x^2\) + 4x - 175 = 0 (quadratic) Factorising, (x - 7) (3x + 25) = 0, either x = 7 or x = -25/3 ( but x cannot be negative) Therefore, x = 7.