Thread: Finding unknown base from equation

I am given this equation of an unknown base:

It has a solution of x=5 and x=8 which are likely to be in our base 10.

I tried to find out the unknown base by comparing the co-efficients of the equations by doing so:
<--in base 10
<--in unknown base

Then I try to solve for the unknown base:
1*b = 13, b=13
but...
5*1 + 2*b = 40
2b = 35
b=17.5

How can the b in the equations be different? If this is the case, what is the actual base for the equation?
thanks!

Originally Posted by xEnOn

I am given this equation of an unknown base:

It has a solution of x=5 and x=8 which are likely to be in our base 10.

I tried to find out the unknown base by comparing the co-efficients of the equations by doing so:
<--in base 10
<--in unknown base

Then I try to solve for the unknown base:
1*b = 13, b=13
but...
5*1 + 2*b = 40
2b = 35
b=17.5

How can the b in the equations be different? If this is the case, what is the actual base for the equation?
thanks!

The equations you bet are inconsistent, which is what I find. So there is no solution to the problem as you post it.

Check the exact wording of the question, and post that.

Also this is not a number theory question, so I am moving the thread to the algebra section.

CB

Thanks for moving to the correct section.

The equation from the question was: in an unknown base with x=5 and x=8.
The question was to find the unknown base of the question. I divided by 5 on the coefficients before trying to find out the base.

Originally Posted by xEnOn

Thanks for moving to the correct section.

The equation from the question was: in an unknown base with x=5 and x=8.
The question was to find the unknown base of the question. I divided by 5 on the coefficients before trying to find out the base.

Now use the same method as before, so in base 10:



and this time it works.

CB

thanks CaptainBlack.
But what is the reason for adding a b this way? And why wouldn't my previous method work?

I calculated the equation and for (5b)x, b=13 but the b^2 + 2b +5, b=13.892 or -13.892. So is 13 considered the base enough though there is 0.892 more?

ok i figured out how the 'b's come into the equation. but still, I am getting b=13 from 5b and b=13.892 or b=-13.892 from . It is weird that the 2 don't give similar results. then how can I determine its base?

Originally Posted by xEnOn

ok i figured out how the 'b's come into the equation. but still, I am getting b=13 from 5b and b=13.892 or b=-13.892 from . It is weird that the 2 don't give similar results. then how can I determine its base?

Your arithmetic is wrong, is a root of

CB

oh yea! you are right about that. I had some calculation mistakes earlier..
thank you so much!