Base of Number System: 121 = 324 Decimal

[mmekosh]

Homework Statement

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

Homework Equations

The Attempt at a Solution

Can you please just explain to me what this means? I don't think we've learned it, and all the explanations I have found online are no help. I have no clue what the question is asking, but if someone could please reword perhaps what the question is asking, I'm sure I could figure it out. Thanks so much!

 

[jegues]

We count using base 10. The decimal number 324 can be defined as follows:

3*(10^2) + 2*(10^1) + 4(10^0) = 324.

So,

324 = 1*(X^2) + 2*(X^1) + 1*(X^0)

This is now a quadratic equation which you can solve. The CORRECT resulting zero will be the base of the system in which the number 121 corresponds to 324 in base 10.

 

[Mark44]

The digits in a number in the decimal (base-10) system represent increasingly higher powers of 10. The decimal number in this problem, 324, represents 3*10² + 2*10¹ + 4*10⁰, or 300 + 20 + 4.

What this problem is asking for is the base b for which 1*b² + 2*b + 1 is the same number as 324. One way to do this problem is trial and error - take a guess at what b might be, and see what 121_b equal as a base-10 number.

Hint: Try values for b that are larger than 10.

 

[mmekosh]

Ok, thank you so much! This helped a lot.