## anonymous one year ago In some number base b, the number 121 is equal to the decimal (base-10) number 324. Calculate b.

1. amilapsn

By solving this you can find $$b$$: $1\times b^2+2\times b^1+1\times b^0=324_{10}$

2. 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)

3. anonymous

Okay but I'm not quite understanding how you guys got that formula...

4. anonymous

the x^2 + 2x + 1 = 324 part...

5. 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

6. anonymous

Thank you so much (: