Changing (123) base 5 into base 10. = 1 x 52 + 2 x 51 + 3 x 50 = 1 x 25 + 2 x 5 + 3 x 10 = 25 + 10 + 3 = 38 .,, (i) Changing x8 base y in decimal = x*y1 + 8*y0 = xy + 8 ... (ii) From Eqs. (i) and (ii), we get xy+ 8= 38 xy = 30 So, possible combinations = (1, 30), (2,15), (3,10) but we have 8 present in x8, so base y > 8 Therefore, total soltuion = 3