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Math Help - Logarythimic Proof Help

  1. #1
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    Logarythimic Proof Help

    The question is to prove the "k" in the following queston is equal to: k = 1/10Loge(10/7)
    and the original question is 70 = 100e-k10

    I'll show the steps i have used so far, but i don't understand the next step needed..

    > 70/100 = e-k10
    > 7/10 = e-k10
    > loge(7/10) = -k10

    That is as far as i can get, if you know the next step please respond with the Log law that goes with it, Any help would be appreciated.

    -Medusa
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  2. #2
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    Re: Logarythimic Proof Help

    After further work, i now am just questioning whether a step is mathmatically allowed? Is it possible to go from my last step to

    >loge((10/7)^-1) = -k10

    and from that just perform basic arithmetic to solve?

    >-ln(10/7) = -k10
    >1/10ln(10/7) = k

    Or is one of the steps incorrect?
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  3. #3
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    Re: Logarythimic Proof Help

    All those steps are correct.
    You alternatively could have done this: 7/10=e^-k10 So 7/10=1/e^k10 So e^k10=10/7
    So k10=ln(10/7) So k= 1/10ln(10/7)
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