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Math Help - logarithm equation.

  1. #1
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    logarithm equation.

    \log_{b-1}\frac{n}{b}=p, where n and p are constants. Solve for b.

    Hmmm...

    Presumably I'd have to set both sides as the exponent of base (b-1) to eliminate the log. But then I have a cubic, right?
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  2. #2
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    Quote Originally Posted by scorpion007 View Post
    \log_{b-1}\frac{n}{b}=p, where n and p are constants. Solve for b.

    Hmmm...

    Presumably I'd have to set both sides as the exponent of base (b-1) to eliminate the log. But then I have a cubic, right?
    (b - 1)^p = \frac{n}{b} \Rightarrow b(b - 1)^p - n = 0.

    What happens next will depend on the values of p and n.
    Last edited by mr fantastic; May 28th 2009 at 04:19 AM. Reason: Fixed a typo
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  3. #3
    Senior Member Sampras's Avatar
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    Quote Originally Posted by mr fantastic View Post
    (b - 1)^p = \frac{n}{p} \Rightarrow b(b - 1)^p - n = 0.

    What happens next will depend on the values of p and n.
     (b-1)^{p} = \frac{n}{b} .
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