Find the value of x for which 32 base =22 base five?

Answer 1

You want 32_x = 22₅ ?
3x + 2 = 2(5) + 2
3x = 10

x = 10/3

mmmhhh, bases of number systems are usually restricted to whole numbers, but mathematically it works.
32_10/3 in base 10 = 3(10/3) + 2 = 12
22₅ in base 10 = 2(5) + 2 = 12