SOLUTION: If 123 base b =83 solve for b. I would be happy if someone could even just show me the steps, please.

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Question 712639: If 123 base b =83 solve for b.
I would be happy if someone could even just show me the steps, please.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In general, to convert from base b to base 10, you plug the digits a0...an from left to right into the polynomial of the form a0*b^n + ... an*b^0


So that would mean


xyz base b = x*b^2 + y*b^1 + z*b^0

123 base b = 1*b^2 + 2*b^1 + 3*b^0

123 base b = 1*b^2 + 2*b^1 + 3*b^0

123 base b = 1*b^2 + 2*b + 3*b^0

83 = 1*b^2 + 2*b + 3*b^0

1*b^2 + 2*b + 3*b^0 = 83

b^2 + 2b + 3 = 83

b^2 + 2b + 3 - 83 = 0

b^2 + 2b - 80 = 0

(b+10)(b-8) = 0

b+10 = 0 or b-8 = 0

b = -10 or b = 8

Toss out the negative base

The only solution left is b = 8

So 123 base 8 = 83 base 10