# Thread: numbers in different bases

1. ## numbers in different bases

Hi Im studying for finals and Ive been looking up the old exams and one reoccuring question that i cant quite get my head around is for example they give u a number in a base and then give a number thats equal to it in another base and the question is to find the unknown base

eg. (456) in base b = (2201) in base 7
find b.

2. Why is this not just a test of your knowledge of the base positional system?

456 (b) = 2201 (7)

so

4*b*b + 5*b + 6 = 2*7*7*7 + 2*7*7 + 0*7 + 1

Solve for 'b'. In this case, it's only quadratic so you should be able to solve it. Of course, since we need a nice whole number, you should be able to factor it. Further, since you just made this one up, or it's a really odd example, you'll need to find some other way to solve the quadratic.

3. yah when i tried to solve it u get imaginary roots which is really weird since its a question off last years exam. Im not sure what else to do.

4. No, they are Irrational, but Real. That's a bit unusual.

Not every question is designed perfectly. Not every answer is neat and clean.