Each of x₁, x₂ and x₃ corresponds to a nonzero digit, whether same or different, in positive integer base b.

Determine all possible value(s) of b ≤ 100 such that this equation has at least one valid solution:

x₁x₂x₃ = x₁^x₁ + x₂^x₂ + x₃^x₃

Note: x₁x₂x₃ corresponds to concatenation of the three digits.