Find n if 34n 100112 - JAMB Mathematics 1992 Question

To find n if 34n = 10011₂, convert both sides to base 10

= 3n + 4 = (1 x 2⁴) + (0 x2³) + (0 x 2²) + (1 x 2¹) + 1 x 2^o

= 3n + 4 = 16 + 0 + 0 + 2 + 1

3n + 4 = 19

3n = 15

n = 5