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Math Help - simple simplification

  1. #1
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    simple simplification

    Im just confused as to how this step (1) [ -ln l 150 - y l = (t / 200) - ln 130 ], simplified into this (2) l 150 - y l = 130e^(-t/200)

    The only part i dont understand about this is how (t/200) in (1) became (-t/200) in (2)



    Thanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by johntuan View Post
    Im just confused as to how this step (1) [ -ln l 150 - y l = (t / 200) - ln 130 ], simplified into this (2) l 150 - y l = 130e^(-t/200)

    The only part i dont understand about this is how (t/200) in (1) became (-t/200) in (2)



    Thanks
    Note that -\ln\left|150-y\right|=\frac{t}{200}-\ln 130\implies \ln\left|150-y\right|=-\frac{t}{200}+\ln 130

    So \left|150-y\right|=e^{-\frac{t}{200}+\ln 130}=e^{-\frac{t}{200}}e^{\ln 130}=130e^{-\frac{t}{200}}

    Does this make sense?
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