Question 712639
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



<font color="red">x</font><font color="blue">y</font><font color="green">z</font> base b = <font color="red">x</font>*b^2 + <font color="blue">y</font>*b^1 + <font color="green">z</font>*b^0


<font color="red">1</font><font color="blue">2</font><font color="green">3</font> base b = <font color="red">1</font>*b^2 + <font color="blue">2</font>*b^1 + <font color="green">3</font>*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 <font color="red">8</font> = 83 base 10