In some number base b, the number 121 is equal to the decimal (base-10) number 324. Calculate b.

Question

amilapsn · Answer

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

phi · Answer

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 · Answer

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

anonymous · Answer

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

phi · Answer

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 · Answer

Thank you so much (: