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# Another question

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94
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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?

Apr 2, 2021

#1
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Using base a expansion, we get a^2 - 11a - 26 = 0.  This factors as (a - 13)(a + 2) = 0, so a = 13.

Apr 2, 2021
#2
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sorry, that was incorrect. Is there a way to do this problem?

Edit: Nevertheless, I realized I made a calculation mistake, and I had found that the answer is a=12

OofPirate  Apr 2, 2021
edited by OofPirate  Apr 2, 2021
#3
+113190
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Melody  Apr 2, 2021
#4
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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
edited by OofPirate  Apr 2, 2021
#5
+113190
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Thanks OP

I like the calculator that you have found

This can be found at the end of the  "Sticky Topics" list on the right of the web2 site.

Melody  Apr 3, 2021
edited by Melody  Apr 3, 2021
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+87
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oh! and forgot to mention: For that tool link, there's a number conversion table, so you can compare all bases up to base 36.

http://www.unitconversion.org/unit_converter/numbers-ex.html

OofPirate  Apr 3, 2021