# What is the base of the system...

• Mar 19th 2007, 12:17 PM
ceasar_19134
What is the base of the system...
What is the base of the system in which 121 represents the same number as the decimal number 324?
• Mar 19th 2007, 12:52 PM
Plato
Solve b^2 + 2b + 1 = 324.
• Mar 28th 2007, 03:14 PM
Rimas
Quote:

Originally Posted by Plato
Solve b^2 + 2b + 1 = 324.

How did you get that??
• Mar 28th 2007, 05:32 PM
topsquark
Quote:

Originally Posted by ceasar_19134
What is the base of the system in which 121 represents the same number as the decimal number 324?

Quote:

Originally Posted by Plato
Solve b^2 + 2b + 1 = 324.

Quote:

Originally Posted by Rimas
How did you get that??

The number 121 in, say base 10, takes the form
1*10^2 + 2*10^1 + 1* 10^0 = 1*100 + 2*10 + 1 = 121

In a base "b" the number 121 represents:
1*b^2 + 2*b^1 + 1*b^0 = b^2 + 2b + 1

(So 121 in base 3 represents the decimal number 3^2 + 2*3 + 1 = 9 + 6 + 1 = 16.)

For this number to be equal to the decimal number 324 we must have
b^2 + 2b + 1 = 324

-Dan