x = 6 explaination : (135)base x + (144) base x = (323)base x means... (1x^2 + 3x + 5) + (1x^2 + 4x + 4) = (3x^2 + 2x + 3) ...... then .... 2x^2 + 7x + 9 = 3x^2 + 2x + 3 x^2 - 5x - 6 = 0 ...... by division method we get ... (x-6)(x+1)=0 so .... as x must be positive ..x=6