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Math Help - solving an exponential equation

  1. #1
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    solving an exponential equation

    A=P(index0)10^r
    If A=80, P(index0)=90, find r

    Here's what I did:
    A=P(index0)10^r
    80=90^r
    ln80=ln90^r
    r=ln80/ln90
    so I get r= 0.973 but actually the solution is supposed to be r=log(8/9) or -0.051153.

    What did I do wrong?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by tami-chan87 View Post
    A=P(index0)10^r
    If A=80, P(index0)=90, find r

    Here's what I did:
    A=P(index0)10^r
    80=90(10^r)
    ln80=ln90^r
    r=ln80/ln90
    so I get r= 0.973 but actually the solution is supposed to be r=log(8/9) or -0.051153.

    What did I do wrong?
    You forgot that r was the exponent of 10, not 90.

    Thus, \tfrac{80}{90}=10^r

    Since \log (x) = \log_{10} (x), we can take the logs of both sides:

    \log\left(\tfrac{8}{9}\right)=\log\left(10^r\right  )\implies \color{red}\boxed{r=\log\left(\tfrac{8}{9}\right)}

    Does this make sense?

    --Chris
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  3. #3
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    Yeah, thanks for your help
    Last edited by tami-chan87; July 31st 2008 at 10:15 AM.
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