If I'm understanding the question correctly, you are looking for an integer b (b ≠ 0, b ≠ 1) such that
[tex]34_b = 22_{10}[/tex]
In other words, you're solving for b such that
3×b ¹ + 4×b ⁰ = 22
or
3b + 4 = 22
Solving this is trivial:
3b + 4 = 22
3b = 18
b = 6
So we have
34₆ = 22₁₀
