anonymous
  • anonymous
In some number base b, the number 121 is equal to the decimal (base-10) number 324. Calculate b.
Mathematics
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anonymous
  • anonymous
In some number base b, the number 121 is equal to the decimal (base-10) number 324. Calculate b.
Mathematics
chestercat
  • chestercat
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amilapsn
  • amilapsn
By solving this you can find \(b\): \[1\times b^2+2\times b^1+1\times b^0=324_{10}\]
phi
  • phi
to make the problem look more familiar, remember any base to the 0 power is 1 \( b^0= 1\) rather than b let's use x (again to make this look familiar) then amilapsn expression can be written as \[ x^2 +2x +1 = 324\\ x^2 +2x-323= 0\] it is a bit ugly, but it does factor. (hint: divide 17 into 323)
anonymous
  • anonymous
Okay but I'm not quite understanding how you guys got that formula...

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anonymous
  • anonymous
the x^2 + 2x + 1 = 324 part...
phi
  • phi
a number to the base x is by definition (which means you have to memorize this) has digits that represent powers of base x for example, if you have 3 digits (in base x) abc that means a*x^2 + b*x^1 + c*x^0 for example, 123 in base 10 means 1*10^2 + 2*10^1 + 3*10^0
anonymous
  • anonymous
Thank you so much (:

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