TITLE: How to find the radix (base) of a number given its representation in another radix (base)?
QUESTION [9 upvotes]: What's the method to find the base of any given number?
E.g. find $r$ such that $(121)_r=(144)_8$, where $r$ and $8$ are the bases.
So how do I find the value of $r$?

REPLY [5 votes]: remember the bold letters are the powers

(121)r=(144)8

Now r and 8 is the base so,
$1\cdot r^2+2 \cdot r^1+1\cdot r^0 = 1 \cdot 8^2+4\cdot 8^1+4 \cdot 8^0$

$r^2+2r+1=64+32+4$

$r^2+2r+1=100$

$(r+1)² =100$

$r+1=10$

$r= 10-1$

$r=9$