Hi! I got stuck here:

Find the value of $a$ that satisfies the equation $293_{a}+468_{a}=73B_{a}$, where $B_{a}=11_{10}$.

I don't really know where to start and what to do. Perhaps you guys can help?

OofPirate Apr 2, 2021

#1**0 **

Using base a expansion, we get a^2 - 11a - 26 = 0. This factors as (a - 13)(a + 2) = 0, so a = 13.

Guest Apr 2, 2021

#4**+3 **

I didn't use an algebraic way, but I used a base change calculator, so essentially guess and check.

However I knew that the base had to be above 11, since B is not included in the Base 11 digits.

Here's a good tool: http://www.unitconversion.org/unit_converter/numbers-ex.html

OofPirate
Apr 2, 2021