Question

The base on which the number n=(34)? is written if it has a value of n= (22)10​

Answer 1

If I'm understanding the question correctly, you are looking for an integer b (b ≠ 0, b ≠ 1) such that

$34_b = 22_{10}$

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