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Math Help - Solving For Non-Integer Bases

  1. #1
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    Solving For Non-Integer Bases

    Hello there first-time poster here!

    First of all, my apologies if this is the wrong forum to post in, my question pertains to a computer science math class, but I'm not quite sure which discipline of math it falls under.

    Anywho, my question is, how can you solve for a non-integer number base, given everything but said base itself?

    I have a number in base 10, (84) and a number in base b (234) and I have to solve for b. 8410 = 234b

    If anyone could point me in the right direction on how to solve this, I would be very thankful.

    Thank you in advance!
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  2. #2
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    Re: Solving For Non-Integer Bases

    Hello, rlp22!

    I have a number 84 in base 10, and a number in base b (234) and I have to solve for b.
    . . 8410 = 234b

    If anyone could point me in the right direction on how to solve this, I would be very thankful.
    Thank you in advance!

    \text{Recall that }234_b\text{ means }2b^2 + 3b + 4


    \text{So we have: }\:2b^2 + 3b + 4 \:=\:84 \quad\Rightarrow\quad 2b^2 + 3b - 80 \:=\:0

    Quadratic Formula: . b \;=\;\dfrac{-3 \pm\sqrt{649}}{4}
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